Anzeige
Erschienen in:
19.05.2022 | Original Paper
Construction of quasi self-dual codes over a commutative non-unital ring of order 4
Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 3/2024
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
Let I be the commutative non-unital ring of order 4 defined by generators and relations. Alahmadi et al. have classified QSD codes, Type IV codes (QSD codes with even weights) and quasi-Type IV codes (QSD codes with even torsion code) over I up to lengths \(n=6\), and suggested two building-up methods for constructing QSD codes. In this paper, we construct more QSD codes, Type IV codes and quasi-Type IV codes for lengths \(n=7\) and 8, and describe five new variants of the two building-up construction methods. We find that when \(n=8\) there is at least one QSD code with minimun distance 4, which attains the highest minimum distance so far, and we give a generator matrix for the code. We also describe some QSD codes, Type IV codes and quasi-Type IV codes with new weight distributions.
$$\begin{aligned} I=\left\langle a,b\mid 2a=2b=0,\,a^{2}=b,\,ab=0\right\rangle . \end{aligned}$$