<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>-linear codes over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>-algebras

Mahmoudi, Saadoun; Mirmohammadirad, Fahime; Samei, Karim

doi:10.1016/j.ffa.2020.101665

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…It is easy to see that S is an F q -module (F q vector space), where the scalar multiplication is defined as follows: for a ∈ F q and s ∈ S, we have a.s = f (a)s ∈ S. For a positive integer n, a subset C ⊆ S n is called an F q -linear code of length n over S if C is an F q -submodule of S n . This class of codes has been studied in [5].…”

Section: Preliminariesmentioning

confidence: 99%

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Every Fq -linear code is equivalent to a non-trivial multi-twisted code

Samei

Mahmoudi

2022

Preprint

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Aydina and Halilovi\'{c} [Finite fields Appl. 45 (2017) 96-106] introduced multi-twisted codes and studied some of their basic properties. Let S be a finite commutative Fq-algebra. An Fq-linear code over S of length n is an Fq-submodule of Sn. Recently, Mahmoudi et al. [Finite fields Appl. 64 (2020) 101665] studied Fq-linear codes over Fq-algebras. In this paper, we show that every Fq-linear code is equivalent to a multi-twisted (MT) code. This gives us a new point of view to study linear codes. In particular, we can investigate the structure of multi-twisted codes instead of Fq-linear codes. 2000 Mathematics subject classification: 94B15, 16S36.

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Section: Preliminariesmentioning

confidence: 99%

“…to C with the following generator matrix 4), and C ′′ = C ′(3,id,3,id,id,(1,2) (3,4)) is an equivalent code to C ′ with the following generator matrix Also C ′′ = C ′(id,id,4,id,id,id,id,id,(1,2)(3,4) (5,6)) is an equivalent code to C ′ with the following generator matrix…”

Section: Statements and Declarationsmentioning

confidence: 99%

Every Fq -linear code is equivalent to a non-trivial multi-twisted code

Samei

Mahmoudi

2022

Preprint

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Every $ \mathbb{F}_q $-linear code is equivalent to a multi-twisted code

Mahmoudi,

Samei

2024

AMC

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Aydina and Halilović (Finite fields Appl. 45 (2017) 96-106) introduced multi-twisted codes and studied some of their basic properties. Let S be a finite commutative Fq-algebra. An Fq-linear code over S of length n is an Fq-submodule of S n . Recently, Mahmoudi et al. (Finite fields Appl. 64 (2020) 101665) studied Fq-linear codes over Fq-algebras. In this paper, we show that every Fq-linear code is equivalent to a multi-twisted (MT) code. This gives us a new point of view in coding theory. In particular, we obtain a rich mathematical structure for linear codes.

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Fq-linear codes over Fq-algebras

Cited by 2 publications

References 16 publications

Every Fq -linear code is equivalent to a non-trivial multi-twisted code

Every Fq -linear code is equivalent to a non-trivial multi-twisted code

Every $ \mathbb{F}_q $-linear code is equivalent to a multi-twisted code

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