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Add quantum tanner codes class #82

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ae6a174
Add a class for Quantum Tanner Codes https://arxiv.org/abs/2202.13641
armandaoq Jul 9, 2025
4ddba71
Add a class for Quantum Tanner Codes https://arxiv.org/abs/2202.13641
armandaoq Jul 9, 2025
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Empty file added quantum_tanner_codes/__init__.py
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47 changes: 47 additions & 0 deletions quantum_tanner_codes/auxiliary/binary_utils.py
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Original file line number Diff line number Diff line change
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import numpy as np
def gaussian_reduction(b):
"""Uses gauss elimination to compute the spaces generated by a matrix over GF(2)\
outputs: rank, a matrix whose rows are a basis of the kernel\
a matrix of independent rows of b, which generate its image\
a matrix of independent rows, that complete the rows of gauss['im']\
to a basis of the space\
the set of pivot row: indices of maximal set of independent row for b"""
a = np.copy(b)
m, n = a.shape
ker = np.eye(n).astype(int)
pivot = set()
pivot_row = set()
for j in range(n):
i = 0
while a[i][j] != 1 and i < m - 1:
i += 1
if a[i][j] == 1:
pivot.add(j)
pivot_row.add(i)
for k in range(j + 1, n):
if a[i][k] == 1:
a[:, k] = (a[:, j] + a[:, k]) % 2
ker[:, k] = (ker[:, j] + ker[:, k]) % 2
indices = [j for j in range(n) if j not in pivot]
ker = (ker[:, indices]).T
rk = len(pivot)
image = b[list(pivot_row), :]
complete_to_basis = np.eye(n).astype(int)[indices, :]
return {'rank': rk, 'ker': ker, 'im': image, 'complete_to_basis': complete_to_basis, 'pivot_row': pivot_row,
'indices': indices}


def get_support(m):
"""
A matrix, print support as pair
:param m:
:return:
"""
indices = m.nonzero()
if len(indices) == 2:
rows, cols = indices
out = [(rows[i], cols[i]) for i in range(len(rows))]
else:
rows = indices[0]
out = [rows[i] for i in range(len(rows))]
return out
205 changes: 205 additions & 0 deletions quantum_tanner_codes/auxiliary/group_tables.py
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"""
Here we save some group tables for testing.
Group tables are as per GAP output MultiplicationTable(G), where G is a group.
The identity here is element 0, while in gap is element 1, so all the tables are shifted for consistence
i.e. table = gap_table - 1
"""

import numpy as np


klein_table = np.array([[1, 2, 3, 4],
[2, 1, 4, 3],
[3, 4, 1, 2],
[4, 3, 2, 1]])

klein_table = klein_table - 1

quaternion = np.array([[1, 2, 3, 4, 5, 6, 7, 8],
[2, 4, 5, 6, 7, 1, 8, 3],
[3, 8, 4, 7, 2, 5, 1, 6],
[4, 6, 7, 1, 8, 2, 3, 5],
[5, 3, 6, 8, 4, 7, 2, 1],
[6, 1, 8, 2, 3, 4, 5, 7],
[7, 5, 1, 3, 6, 8, 4, 2],
[8, 7, 2, 5, 1, 3, 6, 4]])

quaternion = quaternion - 1

quaternion_3 = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[2, 3, 5, 6, 1, 7, 9, 10, 4, 11, 12, 8],
[3, 5, 1, 7, 2, 9, 4, 11, 6, 12, 8, 10],
[4, 10, 7, 8, 12, 2, 11, 1, 5, 6, 3, 9],
[5, 1, 2, 9, 3, 4, 6, 12, 7, 8, 10, 11],
[6, 11, 9, 10, 8, 3, 12, 2, 1, 7, 5, 4],
[7, 12, 4, 11, 10, 5, 8, 3, 2, 9, 1, 6],
[8, 6, 11, 1, 9, 10, 3, 4, 12, 2, 7, 5],
[9, 8, 6, 12, 11, 1, 10, 5, 3, 4, 2, 7],
[10, 7, 12, 2, 4, 11, 5, 6, 8, 3, 9, 1],
[11, 9, 8, 3, 6, 12, 1, 7, 10, 5, 4, 2],
[12, 4, 10, 5, 7, 8, 2, 9, 11, 1, 6, 3]])

quaternion_3 = quaternion_3 - 1

quaternion_4 = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16],
[2, 5, 6, 7, 8, 10, 11, 1, 12, 13, 14, 15, 3, 4, 16, 9],
[3, 12, 5, 9, 10, 7, 13, 16, 11, 1, 15, 8, 14, 6, 4, 2],
[4, 14, 15, 5, 11, 12, 2, 7, 3, 9, 1, 13, 16, 8, 10, 6],
[5, 8, 10, 11, 1, 13, 14, 2, 15, 3, 4, 16, 6, 7, 9, 12],
[6, 15, 8, 12, 13, 11, 3, 9, 14, 2, 16, 1, 4, 10, 7, 5],
[7, 4, 16, 8, 14, 15, 5, 11, 6, 12, 2, 3, 9, 1, 13, 10],
[8, 1, 13, 14, 2, 3, 4, 5, 16, 6, 7, 9, 10, 11, 12, 15],
[9, 6, 4, 10, 15, 8, 12, 13, 5, 11, 3, 14, 2, 16, 1, 7],
[10, 16, 1, 15, 3, 14, 6, 12, 4, 5, 9, 2, 7, 13, 11, 8],
[11, 7, 9, 1, 4, 16, 8, 14, 10, 15, 5, 6, 12, 2, 3, 13],
[12, 10, 7, 13, 16, 1, 15, 3, 8, 14, 6, 4, 5, 9, 2, 11],
[13, 9, 2, 16, 6, 4, 10, 15, 7, 8, 12, 5, 11, 3, 14, 1],
[14, 11, 12, 2, 7, 9, 1, 4, 13, 16, 8, 10, 15, 5, 6, 3],
[15, 13, 11, 3, 9, 2, 16, 6, 1, 4, 10, 7, 8, 12, 5, 14],
[16, 3, 14, 6, 12, 5, 9, 10, 2, 7, 13, 11, 1, 15, 8, 4]])

quaternion_4 = quaternion_4 - 1

quaternion_5 = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
[2, 3, 5, 6, 1, 7, 9, 10, 4, 11, 13, 14, 8, 15, 17, 18, 12, 19, 20, 16],
[3, 5, 1, 7, 2, 9, 4, 11, 6, 13, 8, 15, 10, 17, 12, 19, 14, 20, 16, 18],
[4, 18, 7, 8, 20, 2, 11, 12, 5, 6, 15, 16, 9, 10, 19, 1, 13, 14, 3, 17],
[5, 1, 2, 9, 3, 4, 6, 13, 7, 8, 10, 17, 11, 12, 14, 20, 15, 16, 18, 19],
[6, 19, 9, 10, 16, 3, 13, 14, 1, 7, 17, 18, 4, 11, 20, 2, 8, 15, 5, 12],
[7, 20, 4, 11, 18, 5, 8, 15, 2, 9, 12, 19, 6, 13, 16, 3, 10, 17, 1, 14],
[8, 14, 11, 12, 17, 18, 15, 16, 20, 2, 19, 1, 5, 6, 3, 4, 9, 10, 7, 13],
[9, 16, 6, 13, 19, 1, 10, 17, 3, 4, 14, 20, 7, 8, 18, 5, 11, 12, 2, 15],
[10, 15, 13, 14, 12, 19, 17, 18, 16, 3, 20, 2, 1, 7, 5, 6, 4, 11, 9, 8],
[11, 17, 8, 15, 14, 20, 12, 19, 18, 5, 16, 3, 2, 9, 1, 7, 6, 13, 4, 10],
[12, 10, 15, 16, 13, 14, 19, 1, 17, 18, 3, 4, 20, 2, 7, 8, 5, 6, 11, 9],
[13, 12, 10, 17, 15, 16, 14, 20, 19, 1, 18, 5, 3, 4, 2, 9, 7, 8, 6, 11],
[14, 11, 17, 18, 8, 15, 20, 2, 12, 19, 5, 6, 16, 3, 9, 10, 1, 7, 13, 4],
[15, 13, 12, 19, 10, 17, 16, 3, 14, 20, 1, 7, 18, 5, 4, 11, 2, 9, 8, 6],
[16, 6, 19, 1, 9, 10, 3, 4, 13, 14, 7, 8, 17, 18, 11, 12, 20, 2, 15, 5],
[17, 8, 14, 20, 11, 12, 18, 5, 15, 16, 2, 9, 19, 1, 6, 13, 3, 4, 10, 7],
[18, 7, 20, 2, 4, 11, 5, 6, 8, 15, 9, 10, 12, 19, 13, 14, 16, 3, 17, 1],
[19, 9, 16, 3, 6, 13, 1, 7, 10, 17, 4, 11, 14, 20, 8, 15, 18, 5, 12, 2],
[20, 4, 18, 5, 7, 8, 2, 9, 11, 12, 6, 13, 15, 16, 10, 17, 19, 1, 14, 3]])
quaternion_5 = quaternion_5 - 1

quaternion_6 = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24],
[2, 4, 6, 7, 8, 9, 1, 11, 13, 14, 15, 16, 3, 17, 5, 19, 20, 21, 22, 10, 23, 12, 24, 18],
[3, 13, 4, 9, 10, 2, 6, 20, 1, 11, 17, 18, 7, 8, 14, 24, 5, 19, 23, 15, 16, 21, 12, 22],
[4, 7, 9, 1, 11, 13, 2, 15, 3, 17, 5, 19, 6, 20, 8, 22, 10, 23, 12, 14, 24, 16, 18, 21],
[5, 16, 10, 11, 12, 21, 22, 2, 17, 18, 19, 1, 24, 6, 7, 8, 23, 3, 4, 13, 14, 15, 9, 20],
[6, 3, 7, 13, 14, 4, 9, 10, 2, 15, 20, 21, 1, 11, 17, 18, 8, 22, 24, 5, 19, 23, 16, 12],
[7, 1, 13, 2, 15, 3, 4, 5, 6, 20, 8, 22, 9, 10, 11, 12, 14, 24, 16, 17, 18, 19, 21, 23],
[8, 19, 14, 15, 16, 23, 12, 4, 20, 21, 22, 2, 18, 9, 1, 11, 24, 6, 7, 3, 17, 5, 13, 10],
[9, 6, 1, 3, 17, 7, 13, 14, 4, 5, 10, 23, 2, 15, 20, 21, 11, 12, 18, 8, 22, 24, 19, 16],
[10, 24, 11, 17, 18, 16, 21, 13, 5, 19, 23, 3, 22, 2, 6, 20, 12, 4, 9, 7, 8, 14, 1, 15],
[11, 22, 17, 5, 19, 24, 16, 7, 10, 23, 12, 4, 21, 13, 2, 15, 18, 9, 1, 6, 20, 8, 3, 14],
[12, 8, 18, 19, 1, 14, 15, 16, 23, 3, 4, 5, 20, 21, 22, 2, 9, 10, 11, 24, 6, 7, 17, 13],
[13, 9, 2, 6, 20, 1, 3, 17, 7, 8, 14, 24, 4, 5, 10, 23, 15, 16, 21, 11, 12, 18, 22, 19],
[14, 18, 15, 20, 21, 19, 23, 3, 8, 22, 24, 6, 12, 4, 9, 10, 16, 7, 13, 1, 11, 17, 2, 5],
[15, 12, 20, 8, 22, 18, 19, 1, 14, 24, 16, 7, 23, 3, 4, 5, 21, 13, 2, 9, 10, 11, 6, 17],
[16, 11, 21, 22, 2, 17, 5, 19, 24, 6, 7, 8, 10, 23, 12, 4, 13, 14, 15, 18, 9, 1, 20, 3],
[17, 21, 5, 10, 23, 22, 24, 6, 11, 12, 18, 9, 16, 7, 13, 14, 19, 1, 3, 2, 15, 20, 4, 8],
[18, 20, 19, 23, 3, 8, 14, 24, 12, 4, 9, 10, 15, 16, 21, 13, 1, 11, 17, 22, 2, 6, 5, 7],
[19, 15, 23, 12, 4, 20, 8, 22, 18, 9, 1, 11, 14, 24, 16, 7, 3, 17, 5, 21, 13, 2, 10, 6],
[20, 23, 8, 14, 24, 12, 18, 9, 15, 16, 21, 13, 19, 1, 3, 17, 22, 2, 6, 4, 5, 10, 7, 11],
[21, 10, 22, 24, 6, 11, 17, 18, 16, 7, 13, 14, 5, 19, 23, 3, 2, 15, 20, 12, 4, 9, 8, 1],
[22, 5, 24, 16, 7, 10, 11, 12, 21, 13, 2, 15, 17, 18, 19, 1, 6, 20, 8, 23, 3, 4, 14, 9],
[23, 14, 12, 18, 9, 15, 20, 21, 19, 1, 3, 17, 8, 22, 24, 6, 4, 5, 10, 16, 7, 13, 11, 2],
[24, 17, 16, 21, 13, 5, 10, 23, 22, 2, 6, 20, 11, 12, 18, 9, 7, 8, 14, 19, 1, 3, 15, 4]])

quaternion_6 = quaternion_6 - 1

d12_2 = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24],
[2, 4, 6, 7, 8, 9, 1, 11, 13, 14, 15, 16, 3, 17, 5, 19, 20, 21, 22, 10, 23, 12, 24, 18],
[3, 6, 1, 9, 10, 2, 13, 14, 4, 5, 17, 18, 7, 8, 20, 21, 11, 12, 23, 15, 16, 24, 19, 22],
[4, 7, 9, 1, 11, 13, 2, 15, 3, 17, 5, 19, 6, 20, 8, 22, 10, 23, 12, 14, 24, 16, 18, 21],
[5, 16, 10, 11, 12, 21, 22, 2, 17, 18, 19, 1, 24, 6, 7, 8, 23, 3, 4, 13, 14, 15, 9, 20],
[6, 9, 2, 13, 14, 4, 3, 17, 7, 8, 20, 21, 1, 11, 10, 23, 15, 16, 24, 5, 19, 18, 22, 12],
[7, 1, 13, 2, 15, 3, 4, 5, 6, 20, 8, 22, 9, 10, 11, 12, 14, 24, 16, 17, 18, 19, 21, 23],
[8, 19, 14, 15, 16, 23, 12, 4, 20, 21, 22, 2, 18, 9, 1, 11, 24, 6, 7, 3, 17, 5, 13, 10],
[9, 13, 4, 3, 17, 7, 6, 20, 1, 11, 10, 23, 2, 15, 14, 24, 5, 19, 18, 8, 22, 21, 12, 16],
[10, 21, 5, 17, 18, 16, 24, 6, 11, 12, 23, 3, 22, 2, 13, 14, 19, 1, 9, 7, 8, 20, 4, 15],
[11, 22, 17, 5, 19, 24, 16, 7, 10, 23, 12, 4, 21, 13, 2, 15, 18, 9, 1, 6, 20, 8, 3, 14],
[12, 8, 18, 19, 1, 14, 15, 16, 23, 3, 4, 5, 20, 21, 22, 2, 9, 10, 11, 24, 6, 7, 17, 13],
[13, 3, 7, 6, 20, 1, 9, 10, 2, 15, 14, 24, 4, 5, 17, 18, 8, 22, 21, 11, 12, 23, 16, 19],
[14, 23, 8, 20, 21, 19, 18, 9, 15, 16, 24, 6, 12, 4, 3, 17, 22, 2, 13, 1, 11, 10, 7, 5],
[15, 12, 20, 8, 22, 18, 19, 1, 14, 24, 16, 7, 23, 3, 4, 5, 21, 13, 2, 9, 10, 11, 6, 17],
[16, 11, 21, 22, 2, 17, 5, 19, 24, 6, 7, 8, 10, 23, 12, 4, 13, 14, 15, 18, 9, 1, 20, 3],
[17, 24, 11, 10, 23, 22, 21, 13, 5, 19, 18, 9, 16, 7, 6, 20, 12, 4, 3, 2, 15, 14, 1, 8],
[18, 14, 12, 23, 3, 8, 20, 21, 19, 1, 9, 10, 15, 16, 24, 6, 4, 5, 17, 22, 2, 13, 11, 7],
[19, 15, 23, 12, 4, 20, 8, 22, 18, 9, 1, 11, 14, 24, 16, 7, 3, 17, 5, 21, 13, 2, 10, 6],
[20, 18, 15, 14, 24, 12, 23, 3, 8, 22, 21, 13, 19, 1, 9, 10, 16, 7, 6, 4, 5, 17, 2, 11],
[21, 17, 16, 24, 6, 11, 10, 23, 22, 2, 13, 14, 5, 19, 18, 9, 7, 8, 20, 12, 4, 3, 15, 1],
[22, 5, 24, 16, 7, 10, 11, 12, 21, 13, 2, 15, 17, 18, 19, 1, 6, 20, 8, 23, 3, 4, 14, 9],
[23, 20, 19, 18, 9, 15, 14, 24, 12, 4, 3, 17, 8, 22, 21, 13, 1, 11, 10, 16, 7, 6, 5, 2],
[24, 10, 22, 21, 13, 5, 17, 18, 16, 7, 6, 20, 11, 12, 23, 3, 2, 15, 14, 19, 1, 9, 8, 4]])

d12_2 = d12_2 - 1


table_512 = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
27, 28, 29, 30, 31, 32],
[2, 5, 7, 8, 9, 10, 12, 14, 1, 16, 17, 18, 19, 20, 21, 22, 23, 3, 25, 4, 26, 6, 27, 28, 29, 30,
11, 31, 13, 15, 32, 24],
[3, 7, 6, 11, 12, 13, 10, 17, 18, 19, 15, 16, 1, 23, 24, 25, 21, 22, 2, 27, 28, 29, 26, 4, 5, 31,
30, 8, 9, 32, 14, 20],
[4, 8, 11, 1, 14, 15, 17, 2, 20, 21, 3, 23, 24, 5, 6, 26, 7, 27, 28, 9, 10, 30, 12, 13, 31, 16,
18, 19, 32, 22, 25, 29],
[5, 9, 12, 14, 1, 16, 18, 20, 2, 22, 23, 3, 25, 4, 26, 6, 27, 7, 29, 8, 30, 10, 11, 31, 13, 15,
17, 32, 19, 21, 24, 28],
[6, 10, 13, 15, 16, 1, 19, 21, 22, 2, 24, 25, 3, 26, 4, 5, 28, 29, 7, 30, 8, 9, 31, 11, 12, 14,
32, 17, 18, 20, 23, 27],
[7, 12, 10, 17, 18, 19, 16, 23, 3, 25, 21, 22, 2, 27, 28, 29, 26, 6, 5, 11, 31, 13, 30, 8, 9, 32,
15, 14, 1, 24, 20, 4],
[8, 14, 17, 2, 20, 21, 23, 5, 4, 26, 7, 27, 28, 9, 10, 30, 12, 11, 31, 1, 16, 15, 18, 19, 32, 22,
3, 25, 24, 6, 29, 13],
[9, 1, 18, 20, 2, 22, 3, 4, 5, 6, 27, 7, 29, 8, 30, 10, 11, 12, 13, 14, 15, 16, 17, 32, 19, 21,
23, 24, 25, 26, 28, 31],
[10, 16, 19, 21, 22, 2, 25, 26, 6, 5, 28, 29, 7, 30, 8, 9, 31, 13, 12, 15, 14, 1, 32, 17, 18, 20,
24, 23, 3, 4, 27, 11],
[11, 17, 15, 3, 23, 24, 21, 7, 27, 28, 6, 26, 4, 12, 13, 31, 10, 30, 8, 18, 19, 32, 16, 1, 14, 25,
22, 2, 20, 29, 5, 9],
[12, 18, 16, 23, 3, 25, 22, 27, 7, 29, 26, 6, 5, 11, 31, 13, 30, 10, 9, 17, 32, 19, 15, 14, 1, 24,
21, 20, 2, 28, 4, 8],
[13, 19, 1, 24, 25, 3, 2, 28, 29, 7, 4, 5, 6, 31, 11, 12, 8, 9, 10, 32, 17, 18, 14, 15, 16, 23,
20, 21, 22, 27, 26, 30],
[14, 20, 23, 5, 4, 26, 27, 9, 8, 30, 12, 11, 31, 1, 16, 15, 18, 17, 32, 2, 22, 21, 3, 25, 24, 6,
7, 29, 28, 10, 13, 19],
[15, 21, 24, 6, 26, 4, 28, 10, 30, 8, 13, 31, 11, 16, 1, 14, 19, 32, 17, 22, 2, 20, 25, 3, 23, 5,
29, 7, 27, 9, 12, 18],
[16, 22, 25, 26, 6, 5, 29, 30, 10, 9, 31, 13, 12, 15, 14, 1, 32, 19, 18, 21, 20, 2, 24, 23, 3, 4,
28, 27, 7, 8, 11, 17],
[17, 23, 21, 7, 27, 28, 26, 12, 11, 31, 10, 30, 8, 18, 19, 32, 16, 15, 14, 3, 25, 24, 22, 2, 20,
29, 6, 5, 4, 13, 9, 1],
[18, 3, 22, 27, 7, 29, 6, 11, 12, 13, 30, 10, 9, 17, 32, 19, 15, 16, 1, 23, 24, 25, 21, 20, 2, 28,
26, 4, 5, 31, 8, 14],
[19, 25, 2, 28, 29, 7, 5, 31, 13, 12, 8, 9, 10, 32, 17, 18, 14, 1, 16, 24, 23, 3, 20, 21, 22, 27,
4, 26, 6, 11, 30, 15],
[20, 4, 27, 9, 8, 30, 11, 1, 14, 15, 18, 17, 32, 2, 22, 21, 3, 23, 24, 5, 6, 26, 7, 29, 28, 10,
12, 13, 31, 16, 19, 25],
[21, 26, 28, 10, 30, 8, 31, 16, 15, 14, 19, 32, 17, 22, 2, 20, 25, 24, 23, 6, 5, 4, 29, 7, 27, 9,
13, 12, 11, 1, 18, 3],
[22, 6, 29, 30, 10, 9, 13, 15, 16, 1, 32, 19, 18, 21, 20, 2, 24, 25, 3, 26, 4, 5, 28, 27, 7, 8,
31, 11, 12, 14, 17, 23],
[23, 27, 26, 12, 11, 31, 30, 18, 17, 32, 16, 15, 14, 3, 25, 24, 22, 21, 20, 7, 29, 28, 6, 5, 4,
13, 10, 9, 8, 19, 1, 2],
[24, 28, 4, 13, 31, 11, 8, 19, 32, 17, 1, 14, 15, 25, 3, 23, 2, 20, 21, 29, 7, 27, 5, 6, 26, 12,
9, 10, 30, 18, 16, 22],
[25, 29, 5, 31, 13, 12, 9, 32, 19, 18, 14, 1, 16, 24, 23, 3, 20, 2, 22, 28, 27, 7, 4, 26, 6, 11,
8, 30, 10, 17, 15, 21],
[26, 30, 31, 16, 15, 14, 32, 22, 21, 20, 25, 24, 23, 6, 5, 4, 29, 28, 27, 10, 9, 8, 13, 12, 11, 1,
19, 18, 17, 2, 3, 7],
[27, 11, 30, 18, 17, 32, 15, 3, 23, 24, 22, 21, 20, 7, 29, 28, 6, 26, 4, 12, 13, 31, 10, 9, 8, 19,
16, 1, 14, 25, 2, 5],
[28, 31, 8, 19, 32, 17, 14, 25, 24, 23, 2, 20, 21, 29, 7, 27, 5, 4, 26, 13, 12, 11, 9, 10, 30, 18,
1, 16, 15, 3, 22, 6],
[29, 13, 9, 32, 19, 18, 1, 24, 25, 3, 20, 2, 22, 28, 27, 7, 4, 5, 6, 31, 11, 12, 8, 30, 10, 17,
14, 15, 16, 23, 21, 26],
[30, 15, 32, 22, 21, 20, 24, 6, 26, 4, 29, 28, 27, 10, 9, 8, 13, 31, 11, 16, 1, 14, 19, 18, 17, 2,
25, 3, 23, 5, 7, 12],
[31, 32, 14, 25, 24, 23, 20, 29, 28, 27, 5, 4, 26, 13, 12, 11, 9, 8, 30, 19, 18, 17, 1, 16, 15, 3,
2, 22, 21, 7, 6, 10],
[32, 24, 20, 29, 28, 27, 4, 13, 31, 11, 9, 8, 30, 19, 18, 17, 1, 14, 15, 25, 3, 23, 2, 22, 21, 7,
5, 6, 26, 12, 10, 16]])

table_512 = table_512 - 1
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