engleski

On some self-orthogonal codes from M11

M11 is the smallest of five sporadic simple Mathieu groups. It has 39 non-equivalent transitive permutation representations and among them we will focus on representations on 11, 12, 22, 55, 66, 110, 132, 144 and 165 points. Defining base block of a design as union of orbits of a point stabilizer acting on the set of points, we construct 1-designs, and from them codes. We constructed weakly self-orthogonal 1- designs on less than 165 points (inclusive), and from their incidence matrices, by suitable extension, binary self-orthogonal codes. Also, we generalized this construction to obtain self- orthogonal codes over finite field F_q, where q is prime power. In addition, we constructed binary self- orthogonal codes from the orbit matrices of the weakly self-orthogonal 1-designs under an fix-point-free action of prime order cyclic subgroups of the group M11 ; and generalized this construction for obtaining self-orthogonal codes over finite field F_q: Also, we constructed self-orthogonal codes from the orbit matrices of the previously mentioned designs under an action of prime order cyclic subgroups of M11 which act with points orbits of length 1 and p.

weakly self-orthogonal designs, self-orthogonal codes

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