The hulls of matrix-product codes over commutative rings and applications

Deajim, Abdulaziz; Bouye, Mohamed; Guenda, Kenza

doi:10.1007/s12190-020-01447-z

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…The parameters and decoding capabilities of some of such codes were studied by many authors (see for instance [2,9,10]). Some authors also considered matrix-product codes and some of their properties over certain finite commutative rings (see for instance [1,3,4,7]).…”

Section: Introductionmentioning

confidence: 99%

On self-orthogonality and self-duality of matrix-product codes over commutative rings

Deajim¹,

Bouye²

2021

Turk J Math

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Self-orthogonal codes and self-dual codes, on the one hand, and matrix-product codes, on the other, form important and sought-after classes of linear codes. Combining the two constructions would be advantageous. Adding to this combination the relaxation of the underlying algebraic structures to be commutative rings instead of fields would be even more advantageous. The current article paves a path in this direction. The authors study the problem of self-orthogonality and self-duality of matrix-product codes over a commutative ring with identity. Some methods as well as special matrices are introduced for the construction of such codes. A characterization of such codes in some cases is also given. Some concrete examples as well as applications to torsion codes are presented.

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Section: Introductionmentioning

confidence: 99%

On self-orthogonality and self-duality of matrix-product codes over commutative rings

Deajim¹,

Bouye²

2021

Turk J Math

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LCD matrix product codes with an application

Bhowmick

Bagchi

Bandi

2022

Discrete Math. Algorithm. Appl.

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Matrix product (MP) codes over a finite field [Formula: see text], where [Formula: see text] a prime power, were first introduced by Blackmore and Norton [MP codes over [Formula: see text], Appl. Algebra Engrg. Comm. Comput. 12 (2001) 477–500]. This paper investigates linear complementary dual (LCD) MP codes over finite commutative Frobenius rings. We derive a necessary and sufficient condition for an MP code to have an LCD. We provide some efficient constructions of LCD MP codes. Finally, we have shown an application on cryptography of LCD codes.

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The hulls of matrix-product codes over commutative rings and applications

Cited by 2 publications

References 18 publications

On self-orthogonality and self-duality of matrix-product codes over commutative rings

On self-orthogonality and self-duality of matrix-product codes over commutative rings

LCD matrix product codes with an application

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