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Optimal binary and ternary linear codes with hull dimension one

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Abstract

Hulls of linear codes have been of interest and extensively studied due to their wide applications. In this paper, we focus on constructions and optimality of linear codes with hull dimension one over small finite fields. General constructions for such codes are given together with the analysis on their parameters. Optimal linear \([n,2,d]_q\) codes with hull dimension one are presented for all positive integers \(n\ge 3\) and \(q\in \{2,3\}\). Moreover, for \(q=2\), the enumeration of such optimal codes is given up to equivalence.

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Acknowledgements

The authors would like to thank anonymous referees for useful comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand

    Todsapol Mankean & Somphong Jitman

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  1. Todsapol Mankean
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  2. Somphong Jitman
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Correspondence to Somphong Jitman.

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This research was supported by the Thailand Research Fund and Silpakorn University under Research Grant RSA6280042.

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Mankean, T., Jitman, S. Optimal binary and ternary linear codes with hull dimension one. J. Appl. Math. Comput. 64, 137–155 (2020). https://doi.org/10.1007/s12190-020-01348-1

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  • DOI: https://doi.org/10.1007/s12190-020-01348-1

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