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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Acknowledgements
The authors are very grateful to the anonymous reviewers and the Associate Editor for their valuable comments that highly improved the presentation and quality of this paper. This work was supported by National Natural Science Foundation of China under Grants 11971395 and also by the Central Government Funds for Guiding Local Scientific and Technological Development Under Grant 2021ZYD0001.
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Communicated by M. Buratti.
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Tan, P., Fan, C., Mesnager, S. et al. Linear codes from support designs of ternary cyclic codes. Des. Codes Cryptogr. 90, 681–693 (2022). https://doi.org/10.1007/s10623-021-01001-3
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DOI: https://doi.org/10.1007/s10623-021-01001-3