Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of $M_{11}$

TL;DR

This paper generalizes the construction of self-orthogonal codes from designs, extending to arbitrary fields and utilizing designs invariant under the Mathieu group M11 to produce new codes.

Contribution

It introduces a generalized method for constructing self-orthogonal codes from weakly self-orthogonal designs, including those invariant under M11, over arbitrary fields.

Findings

Constructed self-orthogonal codes over arbitrary fields.

Extended design-based code construction methods.

Produced binary self-orthogonal codes from M11-invariant designs.

Abstract

In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described by Tonchev in [12] in order to obtain self-orthogonal codes over an arbitrary field. We extend construction self-orthogonal codes from orbit matrices of self-orthogonal designs and weakly self-orthogonal 1-designs such that block size is odd and block intersection numbers are even described in [5]. Also, we generalize mentioned construction in order to obtain self-orthogonal codes over an arbitrary field. We construct weakly self-orthogonal designs invariant under an action of Mathieu group $M_{11}$ and, from them, binary self-orthogonal codes.