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Applicable Algebra in Engineering, Communication and Computing
Published in: Applicable Algebra in Engineering, Communication and Computing 1/2023

01-02-2021 | Original Paper

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

Authors: Vedrana Mikulić Crnković, Ivona Traunkar

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 1/2023

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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.
previous article Optimal p-ary cyclic codes with two zeros

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Footnotes
1
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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Crnković, D., Mikulić Crnković, V., Rodrigues, B.G.: On self-orthogonal designs and codes related to Held’s simple group. Adv. Math. Commun. 12, 607–628 (2018)MathSciNetCrossRefMATH
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Crnković, D., Mikulić Crnković, V., Švob, A.: On some transitive combinatorial structures constructed from the unitary group \(U(3,3)\). J. Statist. Plann. Inference 144, 19–40 (2014)MathSciNetCrossRefMATH
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Crnković, D., Mostarac, N.: Self-dual codes from orbit matrices and quotient matrices of combinatorial designs. Dis. Math. 341, 3331–3343 (2018)MathSciNetCrossRefMATH
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Crnković, D., Rodrigues, B.G., Simčić, L., Rukavina, S.: Self-orthogonal codes from orbit matrices of 2-designs. Adv. Math. Commun. 7, 161–174 (2013)MathSciNetCrossRefMATH
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Crnković, D., Rukavina, S.: Self-dual codes from extended orbit matrices of symmetric designs. Des. Codes Cryptogr. 79, 113–120 (2016)MathSciNetCrossRefMATH
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Metadata
Title
Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of
Authors
Vedrana Mikulić Crnković
Ivona Traunkar
Publication date
01-02-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 1/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00484-2

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