engleski

On some self-orthogonal codes from M11

M11 is the smallest of five sporadic simple Mathieu groups and it can be represented as transitive permutation group 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. Precisely, we constructed weakly self- orthogonal 1-designs, 1 and from them, by suitable extension, self-orthogonal codes. We will present weakly self-orthogonal 1-designs and self-orthogonal codes obtained from permutation representation of M11 on less than 165 points (inclusive), and some of their properties. Also, we constructed self- orthogonal codes from some orbit matrices of 1- designs.

Mathieu group, self-orthogonal code, design

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