Matrix-Product Codes over Commutative Rings and Constructions Arising from σ,δ-Codes

Mhammed Boulagouaz, Abdulaziz Deajim and Marco Fontana

Journal of Mathematics, 2021, vol. 2021, 1-10

Abstract: A well-known lower bound (over finite fields and some special finite commutative rings) on the Hamming distance of a matrix-product code (MPC) is shown to remain valid over any commutative ring R. A sufficient condition is given, as well, for such a bound to be sharp. It is also shown that an MPC is free when its input codes are all free, in which case a generator matrix is given. If R is finite, a sufficient condition is provided for the dual of an MPC to be an MPC, a generator matrix for such a dual is given, and characterizations of LCD, self-dual, and self-orthogonal MPCs are presented. Finally, the results of this paper are used along with previous results of the authors to construct novel MPCs arising from σ,δ-codes. Some properties of such constructions are also studied.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5521067

DOI: 10.1155/2021/5521067

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