gf(2) Berlekamp Algorithm

If possible, factor polynomial, including at least one irreducible factor.

f = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111
f = 0x00000000000000009aba68ef0cf5c2bf
f = x63 + x60 + x59 + x57 + x55 + x53 + x52 + x51 + x49 + x46 + x45 + x43 + x39 + x38 + x37 + x35 + x34 + x33 + x32 + x27 + x26 + x23 + x22 + x21 + x20 + x18 + x16 + x15 + x14 + x9 + x7 + x5 + x4 + x3 + x2 + x + 1

Calculate vn = x2n (mod f) for n=0 to 63

v0 = x0 (mod f)
v0 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
v0 = 0x00000000000000000000000000000001
v0 = 1

v1 = x2 (mod f)
v1 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100
v1 = 0x00000000000000000000000000000004
v1 = x2

v2 = x4 (mod f)
v2 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000
v2 = 0x00000000000000000000000000000010
v2 = x4

v3 = x6 (mod f)
v3 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000
v3 = 0x00000000000000000000000000000040
v3 = x6

v4 = x8 (mod f)
v4 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000
v4 = 0x00000000000000000000000000000100
v4 = x8

v5 = x10 (mod f)
v5 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000
v5 = 0x00000000000000000000000000000400
v5 = x10

v6 = x12 (mod f)
v6 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000
v6 = 0x00000000000000000000000000001000
v6 = x12

v7 = x14 (mod f)
v7 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000
v7 = 0x00000000000000000000000000004000
v7 = x14

v8 = x16 (mod f)
v8 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000
v8 = 0x00000000000000000000000000010000
v8 = x16

v9 = x18 (mod f)
v9 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000
v9 = 0x00000000000000000000000000040000
v9 = x18

v10 = x20 (mod f)
v10 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000
v10 = 0x00000000000000000000000000100000
v10 = x20

v11 = x22 (mod f)
v11 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000
v11 = 0x00000000000000000000000000400000
v11 = x22

v12 = x24 (mod f)
v12 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000
v12 = 0x00000000000000000000000001000000
v12 = x24

v13 = x26 (mod f)
v13 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000
v13 = 0x00000000000000000000000004000000
v13 = x26

v14 = x28 (mod f)
v14 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000
v14 = 0x00000000000000000000000010000000
v14 = x28

v15 = x30 (mod f)
v15 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000
v15 = 0x00000000000000000000000040000000
v15 = x30

v16 = x32 (mod f)
v16 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000
v16 = 0x00000000000000000000000100000000
v16 = x32

v17 = x34 (mod f)
v17 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000
v17 = 0x00000000000000000000000400000000
v17 = x34

v18 = x36 (mod f)
v18 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000
v18 = 0x00000000000000000000001000000000
v18 = x36

v19 = x38 (mod f)
v19 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000
v19 = 0x00000000000000000000004000000000
v19 = x38

v20 = x40 (mod f)
v20 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000
v20 = 0x00000000000000000000010000000000
v20 = x40

v21 = x42 (mod f)
v21 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000
v21 = 0x00000000000000000000040000000000
v21 = x42

v22 = x44 (mod f)
v22 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000
v22 = 0x00000000000000000000100000000000
v22 = x44

v23 = x46 (mod f)
v23 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000
v23 = 0x00000000000000000000400000000000
v23 = x46

v24 = x48 (mod f)
v24 = b00000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000
v24 = 0x00000000000000000001000000000000
v24 = x48

v25 = x50 (mod f)
v25 = b00000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000
v25 = 0x00000000000000000004000000000000
v25 = x50

v26 = x52 (mod f)
v26 = b00000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000
v26 = 0x00000000000000000010000000000000
v26 = x52

v27 = x54 (mod f)
v27 = b00000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000
v27 = 0x00000000000000000040000000000000
v27 = x54

v28 = x56 (mod f)
v28 = b00000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000
v28 = 0x00000000000000000100000000000000
v28 = x56

v29 = x58 (mod f)
v29 = b00000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000
v29 = 0x00000000000000000400000000000000
v29 = x58

v30 = x60 (mod f)
v30 = b00000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000
v30 = 0x00000000000000001000000000000000
v30 = x60

v31 = x62 (mod f)
v31 = b00000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000
v31 = 0x00000000000000004000000000000000
v31 = x62

v32 = x64 (mod f)
v32 = b00000000000000000000000000000000000000000000000000000000000000000011010101110100110100011101111000011001111010111000010101111110
v32 = 0x00000000000000003574d1de19eb857e
v32 = x61 + x60 + x58 + x56 + x54 + x53 + x52 + x50 + x47 + x46 + x44 + x40 + x39 + x38 + x36 + x35 + x34 + x33 + x28 + x27 + x24 + x23 + x22 + x21 + x19 + x17 + x16 + x15 + x10 + x8 + x6 + x5 + x4 + x3 + x2 + x

v33 = x66 (mod f)
v33 = b00000000000000000000000000000000000000000000000000000000000000000100111101101001001011111001011101101011010110111101011101000111
v33 = 0x00000000000000004f692f976b5bd747
v33 = x62 + x59 + x58 + x57 + x56 + x54 + x53 + x51 + x48 + x45 + x43 + x42 + x41 + x40 + x39 + x36 + x34 + x33 + x32 + x30 + x29 + x27 + x25 + x24 + x22 + x20 + x19 + x17 + x16 + x15 + x14 + x12 + x10 + x9 + x8 + x6 + x2 + x + 1

v34 = x68 (mod f)
v34 = b00000000000000000000000000000000000000000000000000000000000000000000100011010000011011111000001110110100100001001101100001100010
v34 = 0x000000000000000008d06f83b484d862
v34 = x59 + x55 + x54 + x52 + x46 + x45 + x43 + x42 + x41 + x40 + x39 + x33 + x32 + x31 + x29 + x28 + x26 + x23 + x18 + x15 + x14 + x12 + x11 + x6 + x5 + x

v35 = x70 (mod f)
v35 = b00000000000000000000000000000000000000000000000000000000000000000010001101000001101111100000111011010010000100110110000110001000
v35 = 0x00000000000000002341be0ed2136188
v35 = x61 + x57 + x56 + x54 + x48 + x47 + x45 + x44 + x43 + x42 + x41 + x35 + x34 + x33 + x31 + x30 + x28 + x25 + x20 + x17 + x16 + x14 + x13 + x8 + x7 + x3

v36 = x72 (mod f)
v36 = b00000000000000000000000000000000000000000000000000000000000000000001011110111100100100001101010001000100101110000100010010011111
v36 = 0x000000000000000017bc90d444b8449f
v36 = x60 + x58 + x57 + x56 + x55 + x53 + x52 + x51 + x50 + x47 + x44 + x39 + x38 + x36 + x34 + x30 + x26 + x23 + x21 + x20 + x19 + x14 + x10 + x7 + x4 + x3 + x2 + x + 1

v37 = x74 (mod f)
v37 = b00000000000000000000000000000000000000000000000000000000000000000101111011110010010000110101000100010010111000010001001001111100
v37 = 0x00000000000000005ef2435112e1127c
v37 = x62 + x60 + x59 + x58 + x57 + x55 + x54 + x53 + x52 + x49 + x46 + x41 + x40 + x38 + x36 + x32 + x28 + x25 + x23 + x22 + x21 + x16 + x12 + x9 + x6 + x5 + x4 + x3 + x2

v38 = x76 (mod f)
v38 = b00000000000000000000000000000000000000000000000000000000000000000100111010111101110111001001101001010010011011111100110010001110
v38 = 0x00000000000000004ebddc9a526fcc8e
v38 = x62 + x59 + x58 + x57 + x55 + x53 + x52 + x51 + x50 + x48 + x47 + x46 + x44 + x43 + x42 + x39 + x36 + x35 + x33 + x30 + x28 + x25 + x22 + x21 + x19 + x18 + x17 + x16 + x15 + x14 + x11 + x10 + x7 + x3 + x2 + x

v39 = x78 (mod f)
v39 = b00000000000000000000000000000000000000000000000000000000000000000000111110000011101000111011011101010000010101001011011101000110
v39 = 0x00000000000000000f83a3b75054b746
v39 = x59 + x58 + x57 + x56 + x55 + x49 + x48 + x47 + x45 + x41 + x40 + x39 + x37 + x36 + x34 + x33 + x32 + x30 + x28 + x22 + x20 + x18 + x15 + x13 + x12 + x10 + x9 + x8 + x6 + x2 + x

v40 = x80 (mod f)
v40 = b00000000000000000000000000000000000000000000000000000000000000000011111000001110100011101101110101000001010100101101110100011000
v40 = 0x00000000000000003e0e8edd4152dd18
v40 = x61 + x60 + x59 + x58 + x57 + x51 + x50 + x49 + x47 + x43 + x42 + x41 + x39 + x38 + x36 + x35 + x34 + x32 + x30 + x24 + x22 + x20 + x17 + x15 + x14 + x12 + x11 + x10 + x8 + x4 + x3

v41 = x82 (mod f)
v41 = b00000000000000000000000000000000000000000000000000000000000000000110001010000000010100111001101000001001101111101011011011011111
v41 = 0x00000000000000006280539a09beb6df
v41 = x62 + x61 + x57 + x55 + x46 + x44 + x41 + x40 + x39 + x36 + x35 + x33 + x27 + x24 + x23 + x21 + x20 + x19 + x18 + x17 + x15 + x13 + x12 + x10 + x9 + x7 + x6 + x4 + x3 + x2 + x + 1

v42 = x84 (mod f)
v42 = b00000000000000000000000000000000000000000000000000000000000000000010010111001111111101110101100100110011111001001001110010111101
v42 = 0x000000000000000025cff75933e49cbd
v42 = x61 + x58 + x56 + x55 + x54 + x51 + x50 + x49 + x48 + x47 + x46 + x45 + x44 + x42 + x41 + x40 + x38 + x36 + x35 + x32 + x29 + x28 + x25 + x24 + x23 + x22 + x21 + x18 + x15 + x12 + x11 + x10 + x7 + x5 + x4 + x3 + x2 + 1

v43 = x86 (mod f)
v43 = b00000000000000000000000000000000000000000000000000000000000000000000110110000101101101011000101111000011011001111011000001001011
v43 = 0x00000000000000000d85b58bc367b04b
v43 = x59 + x58 + x56 + x55 + x50 + x48 + x47 + x45 + x44 + x42 + x40 + x39 + x35 + x33 + x32 + x31 + x30 + x25 + x24 + x22 + x21 + x18 + x17 + x16 + x15 + x13 + x12 + x6 + x3 + x + 1

v44 = x88 (mod f)
v44 = b00000000000000000000000000000000000000000000000000000000000000000011011000010110110101100010111100001101100111101100000100101100
v44 = 0x00000000000000003616d62f0d9ec12c
v44 = x61 + x60 + x58 + x57 + x52 + x50 + x49 + x47 + x46 + x44 + x42 + x41 + x37 + x35 + x34 + x33 + x32 + x27 + x26 + x24 + x23 + x20 + x19 + x18 + x17 + x15 + x14 + x8 + x5 + x3 + x2

v45 = x90 (mod f)
v45 = b00000000000000000000000000000000000000000000000000000000000000000100001011100001001100000101001100111010100011101100011000001111
v45 = 0x000000000000000042e130533a8ec60f
v45 = x62 + x57 + x55 + x54 + x53 + x48 + x45 + x44 + x38 + x36 + x33 + x32 + x29 + x28 + x27 + x25 + x23 + x19 + x18 + x17 + x15 + x14 + x10 + x9 + x3 + x2 + x + 1

v46 = x92 (mod f)
v46 = b00000000000000000000000000000000000000000000000000000000000000000011111011110000000100001001001011110011110100001001110101000010
v46 = 0x00000000000000003ef01092f3d09d42
v46 = x61 + x60 + x59 + x58 + x57 + x55 + x54 + x53 + x52 + x44 + x39 + x36 + x33 + x31 + x30 + x29 + x28 + x25 + x24 + x23 + x22 + x20 + x15 + x12 + x11 + x10 + x8 + x6 + x

v47 = x94 (mod f)
v47 = b00000000000000000000000000000000000000000000000000000000000000000110000101111010001010101010010011000011101101111011011110110111
v47 = 0x0000000000000000617a2aa4c3b7b7b7
v47 = x62 + x61 + x56 + x54 + x53 + x52 + x51 + x49 + x45 + x43 + x41 + x39 + x37 + x34 + x31 + x30 + x25 + x24 + x23 + x21 + x20 + x18 + x17 + x16 + x15 + x13 + x12 + x10 + x9 + x8 + x7 + x5 + x4 + x2 + x + 1

v48 = x96 (mod f)
v48 = b00000000000000000000000000000000000000000000000000000000000000000010101000100110000100111010001000011011110000001001100100011101
v48 = 0x00000000000000002a2613a21bc0991d
v48 = x61 + x59 + x57 + x53 + x50 + x49 + x44 + x41 + x40 + x39 + x37 + x33 + x28 + x27 + x25 + x24 + x23 + x22 + x15 + x12 + x11 + x8 + x4 + x3 + x2 + 1

v49 = x98 (mod f)
v49 = b00000000000000000000000000000000000000000000000000000000000000000011001000100010001001100110011101100011111101111010011011001011
v49 = 0x00000000000000003222266763f7a6cb
v49 = x61 + x60 + x57 + x53 + x49 + x45 + x42 + x41 + x38 + x37 + x34 + x33 + x32 + x30 + x29 + x25 + x24 + x23 + x22 + x21 + x20 + x18 + x17 + x16 + x15 + x13 + x10 + x9 + x7 + x6 + x3 + x + 1

v50 = x100 (mod f)
v50 = b00000000000000000000000000000000000000000000000000000000000000000101001000110010111100010111001010000011001010110101100110010011
v50 = 0x00000000000000005232f172832b5993
v50 = x62 + x60 + x57 + x53 + x52 + x49 + x47 + x46 + x45 + x44 + x40 + x38 + x37 + x36 + x33 + x31 + x25 + x24 + x21 + x19 + x17 + x16 + x14 + x12 + x11 + x8 + x7 + x4 + x + 1

v51 = x102 (mod f)
v51 = b00000000000000000000000000000000000000000000000000000000000000000111110110111111000101000001010000010101010001101110001100110010
v51 = 0x00000000000000007dbf14141546e332
v51 = x62 + x61 + x60 + x59 + x58 + x56 + x55 + x53 + x52 + x51 + x50 + x49 + x48 + x44 + x42 + x36 + x34 + x28 + x26 + x24 + x22 + x18 + x17 + x15 + x14 + x13 + x9 + x8 + x5 + x4 + x

v52 = x104 (mod f)
v52 = b00000000000000000000000000000000000000000000000000000000000000000101100100110010111010010110000101000000000001011100101100001001
v52 = 0x00000000000000005932e9614005cb09
v52 = x62 + x60 + x59 + x56 + x53 + x52 + x49 + x47 + x46 + x45 + x43 + x40 + x38 + x37 + x32 + x30 + x18 + x16 + x15 + x14 + x11 + x9 + x8 + x3 + 1

v53 = x106 (mod f)
v53 = b00000000000000000000000000000000000000000000000000000000000000000101000110111111011101000101101100011001111111001010100101011010
v53 = 0x000000000000000051bf745b19fca95a
v53 = x62 + x60 + x56 + x55 + x53 + x52 + x51 + x50 + x49 + x48 + x46 + x45 + x44 + x42 + x38 + x36 + x35 + x33 + x32 + x28 + x27 + x24 + x23 + x22 + x21 + x20 + x19 + x18 + x15 + x13 + x11 + x8 + x6 + x4 + x3 + x

v54 = x108 (mod f)
v54 = b00000000000000000000000000000000000000000000000000000000000000000111001110001001000000001011001001111110000110010010000000010110
v54 = 0x0000000000000000738900b27e192016
v54 = x62 + x61 + x60 + x57 + x56 + x55 + x51 + x48 + x39 + x37 + x36 + x33 + x30 + x29 + x28 + x27 + x26 + x25 + x20 + x19 + x16 + x13 + x4 + x2 + x

v55 = x110 (mod f)
v55 = b00000000000000000000000000000000000000000000000000000000000000000110000111101010101110111111100011101101011110101100011110011001
v55 = 0x000000000000000061eabbf8ed7ac799
v55 = x62 + x61 + x56 + x55 + x54 + x53 + x51 + x49 + x47 + x45 + x44 + x43 + x41 + x40 + x39 + x38 + x37 + x36 + x35 + x31 + x30 + x29 + x27 + x26 + x24 + x22 + x21 + x20 + x19 + x17 + x15 + x14 + x10 + x9 + x8 + x7 + x4 + x3 + 1

v56 = x112 (mod f)
v56 = b00000000000000000000000000000000000000000000000000000000000000000010100001100100010101101101001010100000111101010101100110100101
v56 = 0x0000000000000000286456d2a0f559a5
v56 = x61 + x59 + x54 + x53 + x50 + x46 + x44 + x42 + x41 + x39 + x38 + x36 + x33 + x31 + x29 + x23 + x22 + x21 + x20 + x18 + x16 + x14 + x12 + x11 + x8 + x7 + x5 + x2 + 1

v57 = x114 (mod f)
v57 = b00000000000000000000000000000000000000000000000000000000000000000011101100101011001100111010010110001111001000001010010000101011
v57 = 0x00000000000000003b2b33a58f20a42b
v57 = x61 + x60 + x59 + x57 + x56 + x53 + x51 + x49 + x48 + x45 + x44 + x41 + x40 + x39 + x37 + x34 + x32 + x31 + x27 + x26 + x25 + x24 + x21 + x15 + x13 + x10 + x5 + x3 + x + 1

v58 = x116 (mod f)
v58 = b00000000000000000000000000000000000000000000000000000000000000000111011000010110101001100111100100110000011101110101001000010011
v58 = 0x00000000000000007616a67930775213
v58 = x62 + x61 + x60 + x58 + x57 + x52 + x50 + x49 + x47 + x45 + x42 + x41 + x38 + x37 + x36 + x35 + x32 + x29 + x28 + x22 + x21 + x20 + x18 + x17 + x16 + x14 + x12 + x9 + x4 + x + 1

v59 = x118 (mod f)
v59 = b00000000000000000000000000000000000000000000000000000000000000000111011110010100001000001101010111010100110000110000111110001101
v59 = 0x0000000000000000779420d5d4c30f8d
v59 = x62 + x61 + x60 + x58 + x57 + x56 + x55 + x52 + x50 + x45 + x39 + x38 + x36 + x34 + x32 + x31 + x30 + x28 + x26 + x23 + x22 + x17 + x16 + x11 + x10 + x9 + x8 + x7 + x3 + x2 + 1

v60 = x120 (mod f)
v60 = b00000000000000000000000000000000000000000000000000000000000000000111000110011110001110100110011001000110000100100111100111110101
v60 = 0x0000000000000000719e3a66461279f5
v60 = x62 + x61 + x60 + x56 + x55 + x52 + x51 + x50 + x49 + x45 + x44 + x43 + x41 + x38 + x37 + x34 + x33 + x30 + x26 + x25 + x20 + x17 + x14 + x13 + x12 + x11 + x8 + x7 + x6 + x5 + x4 + x2 + 1

v61 = x122 (mod f)
v61 = b00000000000000000000000000000000000000000000000000000000000000000110100110110110010100001010100000001101010101111010000000010101
v61 = 0x000000000000000069b650a80d57a015
v61 = x62 + x61 + x59 + x56 + x55 + x53 + x52 + x50 + x49 + x46 + x44 + x39 + x37 + x35 + x27 + x26 + x24 + x22 + x20 + x18 + x17 + x16 + x15 + x13 + x4 + x2 + 1

v62 = x124 (mod f)
v62 = b00000000000000000000000000000000000000000000000000000000000000000000100100010111111110111001000100100000010000001100011110010101
v62 = 0x00000000000000000917fb912040c795
v62 = x59 + x56 + x52 + x50 + x49 + x48 + x47 + x46 + x45 + x44 + x43 + x41 + x40 + x39 + x36 + x32 + x29 + x22 + x15 + x14 + x10 + x9 + x8 + x7 + x4 + x2 + 1

Represent v0-v62 as matrix Q
Q = 000000000000000000000000000000000000000000000000000000000000001 000000000000000000000000000000000000000000000000000000000000100 000000000000000000000000000000000000000000000000000000000010000 000000000000000000000000000000000000000000000000000000001000000 000000000000000000000000000000000000000000000000000000100000000 000000000000000000000000000000000000000000000000000010000000000 000000000000000000000000000000000000000000000000001000000000000 000000000000000000000000000000000000000000000000100000000000000 000000000000000000000000000000000000000000000010000000000000000 000000000000000000000000000000000000000000001000000000000000000 000000000000000000000000000000000000000000100000000000000000000 000000000000000000000000000000000000000010000000000000000000000 000000000000000000000000000000000000001000000000000000000000000 000000000000000000000000000000000000100000000000000000000000000 000000000000000000000000000000000010000000000000000000000000000 000000000000000000000000000000001000000000000000000000000000000 000000000000000000000000000000100000000000000000000000000000000 000000000000000000000000000010000000000000000000000000000000000 000000000000000000000000001000000000000000000000000000000000000 000000000000000000000000100000000000000000000000000000000000000 000000000000000000000010000000000000000000000000000000000000000 000000000000000000001000000000000000000000000000000000000000000 000000000000000000100000000000000000000000000000000000000000000 000000000000000010000000000000000000000000000000000000000000000 000000000000001000000000000000000000000000000000000000000000000 000000000000100000000000000000000000000000000000000000000000000 000000000010000000000000000000000000000000000000000000000000000 000000001000000000000000000000000000000000000000000000000000000 000000100000000000000000000000000000000000000000000000000000000 000010000000000000000000000000000000000000000000000000000000000 001000000000000000000000000000000000000000000000000000000000000 100000000000000000000000000000000000000000000000000000000000000 011010101110100110100011101111000011001111010111000010101111110 100111101101001001011111001011101101011010110111101011101000111 000100011010000011011111000001110110100100001001101100001100010 010001101000001101111100000111011010010000100110110000110001000 001011110111100100100001101010001000100101110000100010010011111 101111011110010010000110101000100010010111000010001001001111100 100111010111101110111001001101001010010011011111100110010001110 000111110000011101000111011011101010000010101001011011101000110 011111000001110100011101101110101000001010100101101110100011000 110001010000000010100111001101000001001101111101011011011011111 010010111001111111101110101100100110011111001001001110010111101 000110110000101101101011000101111000011011001111011000001001011 011011000010110110101100010111100001101100111101100000100101100 100001011100001001100000101001100111010100011101100011000001111 011111011110000000100001001001011110011110100001001110101000010 110000101111010001010101010010011000011101101111011011110110111 010101000100110000100111010001000011011110000001001100100011101 011001000100010001001100110011101100011111101111010011011001011 101001000110010111100010111001010000011001010110101100110010011 111110110111111000101000001010000010101010001101110001100110010 101100100110010111010010110000101000000000001011100101100001001 101000110111111011101000101101100011001111111001010100101011010 111001110001001000000001011001001111110000110010010000000010110 110000111101010101110111111100011101101011110101100011110011001 010100001100100010101101101001010100000111101010101100110100101 011101100101011001100111010010110001111001000001010010000101011 111011000010110101001100111100100110000011101110101001000010011 111011110010100001000001101010111010100110000110000111110001101 111000110011110001110100110011001000110000100100111100111110101 110100110110110010100001010100000001101010101111010000000010101 000100100010111111110111001000100100000010000001100011110010101
Represent 63x63 identity matrix I
I = 000000000000000000000000000000000000000000000000000000000000001 000000000000000000000000000000000000000000000000000000000000010 000000000000000000000000000000000000000000000000000000000000100 000000000000000000000000000000000000000000000000000000000001000 000000000000000000000000000000000000000000000000000000000010000 000000000000000000000000000000000000000000000000000000000100000 000000000000000000000000000000000000000000000000000000001000000 000000000000000000000000000000000000000000000000000000010000000 000000000000000000000000000000000000000000000000000000100000000 000000000000000000000000000000000000000000000000000001000000000 000000000000000000000000000000000000000000000000000010000000000 000000000000000000000000000000000000000000000000000100000000000 000000000000000000000000000000000000000000000000001000000000000 000000000000000000000000000000000000000000000000010000000000000 000000000000000000000000000000000000000000000000100000000000000 000000000000000000000000000000000000000000000001000000000000000 000000000000000000000000000000000000000000000010000000000000000 000000000000000000000000000000000000000000000100000000000000000 000000000000000000000000000000000000000000001000000000000000000 000000000000000000000000000000000000000000010000000000000000000 000000000000000000000000000000000000000000100000000000000000000 000000000000000000000000000000000000000001000000000000000000000 000000000000000000000000000000000000000010000000000000000000000 000000000000000000000000000000000000000100000000000000000000000 000000000000000000000000000000000000001000000000000000000000000 000000000000000000000000000000000000010000000000000000000000000 000000000000000000000000000000000000100000000000000000000000000 000000000000000000000000000000000001000000000000000000000000000 000000000000000000000000000000000010000000000000000000000000000 000000000000000000000000000000000100000000000000000000000000000 000000000000000000000000000000001000000000000000000000000000000 000000000000000000000000000000010000000000000000000000000000000 000000000000000000000000000000100000000000000000000000000000000 000000000000000000000000000001000000000000000000000000000000000 000000000000000000000000000010000000000000000000000000000000000 000000000000000000000000000100000000000000000000000000000000000 000000000000000000000000001000000000000000000000000000000000000 000000000000000000000000010000000000000000000000000000000000000 000000000000000000000000100000000000000000000000000000000000000 000000000000000000000001000000000000000000000000000000000000000 000000000000000000000010000000000000000000000000000000000000000 000000000000000000000100000000000000000000000000000000000000000 000000000000000000001000000000000000000000000000000000000000000 000000000000000000010000000000000000000000000000000000000000000 000000000000000000100000000000000000000000000000000000000000000 000000000000000001000000000000000000000000000000000000000000000 000000000000000010000000000000000000000000000000000000000000000 000000000000000100000000000000000000000000000000000000000000000 000000000000001000000000000000000000000000000000000000000000000 000000000000010000000000000000000000000000000000000000000000000 000000000000100000000000000000000000000000000000000000000000000 000000000001000000000000000000000000000000000000000000000000000 000000000010000000000000000000000000000000000000000000000000000 000000000100000000000000000000000000000000000000000000000000000 000000001000000000000000000000000000000000000000000000000000000 000000010000000000000000000000000000000000000000000000000000000 000000100000000000000000000000000000000000000000000000000000000 000001000000000000000000000000000000000000000000000000000000000 000010000000000000000000000000000000000000000000000000000000000 000100000000000000000000000000000000000000000000000000000000000 001000000000000000000000000000000000000000000000000000000000000 010000000000000000000000000000000000000000000000000000000000000 100000000000000000000000000000000000000000000000000000000000000
M = Q-I
M = 000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000110 000000000000000000000000000000000000000000000000000000000010100 000000000000000000000000000000000000000000000000000000001001000 000000000000000000000000000000000000000000000000000000100010000 000000000000000000000000000000000000000000000000000010000100000 000000000000000000000000000000000000000000000000001000001000000 000000000000000000000000000000000000000000000000100000010000000 000000000000000000000000000000000000000000000010000000100000000 000000000000000000000000000000000000000000001000000001000000000 000000000000000000000000000000000000000000100000000010000000000 000000000000000000000000000000000000000010000000000100000000000 000000000000000000000000000000000000001000000000001000000000000 000000000000000000000000000000000000100000000000010000000000000 000000000000000000000000000000000010000000000000100000000000000 000000000000000000000000000000001000000000000001000000000000000 000000000000000000000000000000100000000000000010000000000000000 000000000000000000000000000010000000000000000100000000000000000 000000000000000000000000001000000000000000001000000000000000000 000000000000000000000000100000000000000000010000000000000000000 000000000000000000000010000000000000000000100000000000000000000 000000000000000000001000000000000000000001000000000000000000000 000000000000000000100000000000000000000010000000000000000000000 000000000000000010000000000000000000000100000000000000000000000 000000000000001000000000000000000000001000000000000000000000000 000000000000100000000000000000000000010000000000000000000000000 000000000010000000000000000000000000100000000000000000000000000 000000001000000000000000000000000001000000000000000000000000000 000000100000000000000000000000000010000000000000000000000000000 000010000000000000000000000000000100000000000000000000000000000 001000000000000000000000000000001000000000000000000000000000000 100000000000000000000000000000010000000000000000000000000000000 011010101110100110100011101111100011001111010111000010101111110 100111101101001001011111001010101101011010110111101011101000111 000100011010000011011111000011110110100100001001101100001100010 010001101000001101111100000011011010010000100110110000110001000 001011110111100100100001100010001000100101110000100010010011111 101111011110010010000110111000100010010111000010001001001111100 100111010111101110111001101101001010010011011111100110010001110 000111110000011101000110011011101010000010101001011011101000110 011111000001110100011111101110101000001010100101101110100011000 110001010000000010100011001101000001001101111101011011011011111 010010111001111111100110101100100110011111001001001110010111101 000110110000101101111011000101111000011011001111011000001001011 011011000010110110001100010111100001101100111101100000100101100 100001011100001000100000101001100111010100011101100011000001111 011111011110000010100001001001011110011110100001001110101000010 110000101111010101010101010010011000011101101111011011110110111 010101000100111000100111010001000011011110000001001100100011101 011001000100000001001100110011101100011111101111010011011001011 101001000110110111100010111001010000011001010110101100110010011 111110110110111000101000001010000010101010001101110001100110010 101100100100010111010010110000101000000000001011100101100001001 101000110011111011101000101101100011001111111001010100101011010 111001111001001000000001011001001111110000110010010000000010110 110000101101010101110111111100011101101011110101100011110011001 010100101100100010101101101001010100000111101010101100110100101 011100100101011001100111010010110001111001000001010010000101011 111001000010110101001100111100100110000011101110101001000010011 111111110010100001000001101010111010100110000110000111110001101 110000110011110001110100110011001000110000100100111100111110101 100100110110110010100001010100000001101010101111010000000010101 100100100010111111110111001000100100000010000001100011110010101
Find null basis vectors of M

nv0 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
nv0 = 0x00000000000000000000000000000001
nv0 = 1

Only null basis is trivial 1, so f is irreducible.

See also: