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Article Dans Une Revue Journal of Algebra and Its Applications Année : 2021

Type IV codes over a non-unital ring

Alaa Altassan
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Widyan Basaffar
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Alexis Bonnecaze
Hatoon Shoaib
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Patrick Solé

Résumé

There is a special local ring E of order 4, without identity for the multiplication, defined by E = a, b | 2a = 2b = 0, a 2 = a, b 2 = b, ab = a, ba = b. We study the algebraic structure of linear codes over that non-commutative local ring, in particular their residue and torsion codes. We introduce the notion of quasi self-dual codes over E, and Type IV codes, that is quasi self-dual codes whose all codewords have even Hamming weight. We study the weight enumerators of these codes by means of invariant theory, and classify them in short lengths.
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Dates et versions

hal-02433480 , version 1 (09-01-2020)

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  • HAL Id : hal-02433480 , version 1

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Adel Alahmadi, Alaa Altassan, Widyan Basaffar, Alexis Bonnecaze, Hatoon Shoaib, et al.. Type IV codes over a non-unital ring. Journal of Algebra and Its Applications, 2021. ⟨hal-02433480⟩
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