Abstract
In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described in Tonchev (J Combinat Theory Ser A 52:197-205, 1989) 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 Crnković (Adv Math Commun 12:607–628, 2018). 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.
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Notes
Elements which are equal to 0 in \(\mathbb {F}_q\) are also equal to 0 in \(\mathbb {F}_{q^2},\) since elements of \(\mathbb {F}_q\) are polynomials in \(\mathbb {F}_{q^2}\) of degree at most 1 with coefficients in \(\mathbb {F}_q\).
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This work has been supported by Croatian Science Foundation under the project 6732 and by the University of Rijeka under the project uniri-prirod-18-111-1249.
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Mikulić Crnković, V., Traunkar, I. Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of \(M_{11}\). AAECC 34, 139–156 (2023). https://doi.org/10.1007/s00200-020-00484-2
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DOI: https://doi.org/10.1007/s00200-020-00484-2