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Journal of Applied Mathematics and Computing

Erschienen in:

18.04.2020 | Original Research

Optimal binary and ternary linear codes with hull dimension one

verfasst von: Todsapol Mankean, Somphong Jitman

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2020

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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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Titel: Optimal binary and ternary linear codes with hull dimension one
verfasst von: Todsapol Mankean
Somphong Jitman
Publikationsdatum: 18.04.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2020
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01348-1

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