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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 3/2022

14-01-2022

Linear codes from support designs of ternary cyclic codes

Authors: Pan Tan, Cuiling Fan, Sihem Mesnager, Wei Guo

Published in: Designs, Codes and Cryptography | Issue 3/2022

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Abstract

For a long time, the literature has demonstrated that designs and codes are exciting topics for combinatorics and coding theory. Linear codes and t-designs are, in fact, closely related. In recent years, significant results have been derived in the connection framework between codes and combinatorial designs. The most relevant recent contribution is the 71-year breakthrough in discovering by C. Ding and C. Tang of an infinite family of linear codes supporting an infinite family of 4-designs. This paper deals with codes from designs. It considers a class of cyclic codes from the support designs of affine invariant codes and studies ternary cyclic codes. These codes hold 2-designs, contain original affine invariant codes and many other affine-invariant subcodes. The dimension and a lower bound of these ternary cyclic codes are determined.
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Literature
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Ding C.: Designs from Linear Codes. World Scientific, Singapore (2019).MATH
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Ding C., Tang C., Tonchev D.: Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes. Des. Codes Cryptogr. 88, 625–641 (2020).MathSciNetCrossRef
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Ding C., Tang C.: Infinite families of near MDS codes holding \(t\)-designs. IEEE Trans. Inf. Theory 66(9), 5419–5428 (2020).MathSciNetCrossRef
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Ding C.: Infinite families of 3-designs from a type of five-weight code. Des. Codes Cryptogr. 86(3), 703–719 (2018).MathSciNetCrossRef
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Metadata
Title
Linear codes from support designs of ternary cyclic codes
Authors
Pan Tan
Cuiling Fan
Sihem Mesnager
Wei Guo
Publication date
14-01-2022
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 3/2022
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-021-01001-3

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