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

Author

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  • Mhammed Boulagouaz
  • Abdulaziz Deajim
  • Marco Fontana

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.

Suggested Citation

  • Mhammed Boulagouaz & Abdulaziz Deajim & Marco Fontana, 2021. "Matrix-Product Codes over Commutative Rings and Constructions Arising from σ,δ-Codes," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, March.
    • Handle: RePEc:hin:jjmath:5521067
    DOI: 10.1155/2021/5521067
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