×

Constructions and bounds on quaternary linear codes with Hermitian hull dimension one. (English) Zbl 1477.94075

Summary: Due to their practical applications, hulls of linear codes have been of interest and extensively studied. In this paper, we focus on constructions and bounds on quaternary linear codes with Hermitian hull dimension one. Optimal \([n,2]_4\) codes with Hermitian hull dimension one are constructed for all lengths \(n\geq 3\), such that \(n\equiv 1,2,4\pmod 5\). For positive integers \(n\equiv 0,3\pmod 5\), good lower and upper bounds on the minimum weight of quaternary \([n,2]_4\) codes with Hermitian hull dimension one are given.

MSC:

94B05 Linear codes (general theory)
94B65 Bounds on codes
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Assmus, EF; Key, JD, Affine and projective planes, Discrete Math., 83, 161-187 (1990) · Zbl 0707.51012 · doi:10.1016/0012-365X(90)90003-Z
[2] Guenda, K.; Jitman, S.; Gulliver, T., A: Constructions of good entanglement-assisted quantum error correcting codes, Des. Codes Cryptogr., 86, 121-136 (2018) · Zbl 1387.81111 · doi:10.1007/s10623-017-0330-z
[3] Leon, JS, Computing automorphism groups of error-correcting codes, IEEE Trans. Inform. Theory, 28, 496-511 (1982) · Zbl 0479.94016 · doi:10.1109/TIT.1982.1056498
[4] Leon, JS, Permutation group algorithms based on partition, I: theory and algorithms, J. Symb. Comput., 12, 533-583 (1991) · Zbl 0807.20001 · doi:10.1016/S0747-7171(08)80103-4
[5] Luo, G.; Cao, X.; Chen, X., MDS codes with hulls of arbitrary dimensions and their quantum error correction, IEEE Trans. Inform. Theory, 65, 2944-2952 (2019) · Zbl 1431.94161 · doi:10.1109/TIT.2018.2874953
[6] Mankean, T.; Jitman, S., Optimal binary and ternary linear codes with hull dimension one, J. Appl. Math. Comput., 64, 137-155 (2020) · Zbl 1495.94114 · doi:10.1007/s12190-020-01348-1
[7] Pang, B.; Zhu, S.; Kai, X., Some new bounds on LCD codes over finite fields, Cryptogr. Commun., 12, 743-755 (2020) · Zbl 1473.94142 · doi:10.1007/s12095-019-00417-y
[8] Sendrier, N., Skersys, G.: On the computation of the automorphism group of a linear code, in: Proceedings of IEEE ISIT’2001, Washington, DC, p. 13 (2001)
[9] Sendrier, N., On the dimension of the hull, SIAM J. Appl. Math., 10, 282-293 (1997) · Zbl 0868.94040
[10] Sendrier, N., Finding the permutation between equivalent codes: the support splitting algorithm, IEEE Trans. Inform. Theory, 46, 1193-1203 (2000) · Zbl 1002.94037 · doi:10.1109/18.850662
[11] Thipworawimon, S.; Jitman, S., Hulls of linear codes revisited with applications, J. Appl. Math. Comput., 62, 325-340 (2020) · Zbl 1508.94074 · doi:10.1007/s12190-019-01286-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.