Quasi self-dual codes over non-unital rings of order six

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0066

Keywords:

Non-unital rings, Semi-local rings, Self-orthogonal codes, Unimodular lattices

Abstract

There exist two semi-local rings of order 6 without identity for the multiplication. We classify up to coordinate permutation self-orthogonal codes of length n and size 6n/2 over these rings (called here quasi self-dual codes or QSD) till the length n = 8. To any such code is attached canonically a ?6-code, which, when self-dual, produces an unimodular lattice by Construction A.

Author Biographies

Adel Alahmadi, King Abdulaziz University.

Dept. of Mathematics.

Amani Alkathiry, Umm Al-Qura University.

Dept. of Mathematics.

Alaa Altassan, King Abdulaziz University.

Dept. of Mathematics.

Widyan Basaffar, King Abdulaziz University.

Dept. of Mathematics.

Alexis Bonnecaze, Aix-Marseille Université.

CNRS.

Hatoon Shoaib, King Abdulaziz University.

Dept. of Mathematics.

Patrick Solé, Aix-Marseille Université.

CNRS.

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Published

2020-07-28

How to Cite

[1]
A. Alahmadi, “Quasi self-dual codes over non-unital rings of order six”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 1083-1095, Jul. 2020.

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