Quasi type IV codes over a non-unital ring
type: Item
instance of: scholarly article
title: Quasi type IV codes over a non-unital ring
zbMATH Open document ID: 1479.94359
author: Alaa Altassan
author: Widyan Basaffar
author: Alexis Bonnecaze
author: Hatoon Shoaib
author: Patrick Solé
author: Adel Alahmadi
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 2021-08-03T00:00:00Z
review text: The authors introduce codes over a local ring of order \(4\) without identity. Following the notation for codes over \(\mathbb{F}_4\), they call the constructed codes quasi type IV codes. The authors give the general forms of generator matrices (Theorem 1) and parity check matrices (Theorem 2). Further, a construction of QSD codes is given, which the authors call multilevel construction (Theorem 4). In Section 5 of the paper, mass formulas for the constructed QSD codes are proven. Finally, in Section 6, the authors give a short length classification of the introduced codes for \(n\leq 3.\)
reviewed by: Carolin Hannusch
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 16L30
zbMATH DE Number: 7377721
zbMATH Keywords: rings
zbMATH Keywords: codes
zbMATH Keywords: additive \(\mathbb{F}_4\)-codes
zbMATH Keywords: mass formulas
zbMATH Keywords: type IV codes
MaRDI profile type: Publication
full work available at URL: s00200-021-00488-6
OpenAlex ID: W3016550227
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DOI: 10.1007/S00200-021-00488-6
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description: scientific article; zbMATH DE number 7377721