Some binary projective two-weight codes
The binary_projective_two_weight_codes module defines
functions that construct two types of binary projective two-weight codes
as published by Tonchev [Ton1996] [Ton2007].
AUTHORS:
Paul Leopardi (2016-09-15): initial version
EXAMPLES:
sage: from boolean_cayley_graphs.binary_projective_two_weight_codes import binary_projective_two_weight_27_6_12
sage: c27=binary_projective_two_weight_27_6_12()
sage: c27[1]
('000000000000000111111111111',
'000000000111111000000111111',
'000111111000011000011000011',
'001000111011101000101000101',
'010001011101110011101011101',
'100010101000101001111101000')
REFERENCES:
- boolean_cayley_graphs.binary_projective_two_weight_codes.binary_projective_two_weight_27_6_12()[source]
Return the binary projective two-weight [27,6,12] codes as published by Tonchev.
Return a tuple that encodes the generator matrices of the binary projective two-weight [27,6,12] codes, listed as codes 1, 2, 3a, 3b and 4 in Table 1 of Tonchev [Ton1996], and repeated as codes 1 to 5 in Table 1.155 of Tonchev [Ton2007].
INPUT:
None.
OUTPUT:
A tuple of tuples of strings. Each tuple of strings encodes a generator matrix of a binary projective two-weight code.
EXAMPLES:
sage: from boolean_cayley_graphs.binary_projective_two_weight_codes import binary_projective_two_weight_27_6_12 sage: c27=binary_projective_two_weight_27_6_12() sage: c27[0] ('000000000001111111111111111', '000000011110000000011111111', '000001100110000111100001111', '000111111110011001100110011', '011010101010111011101110100', '101010101100001110111011101')
REFERENCES:
- boolean_cayley_graphs.binary_projective_two_weight_codes.binary_projective_two_weight_35_6_16()[source]
Return the binary projective two-weight [35,6,16] codes as published by Tonchev.
Return a tuple that encodes the generator matrices of the binary projective two-weight [35,6,16] codes, listed as codes 1, 2a, 2b, 3a, 3b, 4a and 4b in Table 2 of Tonchev [Ton1996], and repeated as codes 1 to 7 in Table 1.156 of Tonchev [Ton2007].
INPUT:
None.
OUTPUT:
A tuple of tuples of strings. Each tuple of strings encodes a generator matrix of a binary projective two-weight code.
EXAMPLES:
sage: from boolean_cayley_graphs.binary_projective_two_weight_codes import binary_projective_two_weight_35_6_16 sage: c35=binary_projective_two_weight_35_6_16() sage: c35[2] ('00000000000000011111111111111111111', '00000000011111100000000001111111111', '00011111100001100001111110000111111', '00100011101110101110001110111000111', '01000101110111000010110010001011001', '10001010100010110100010100011101011')
REFERENCES: