Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine

We introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic-self-orthogonal and LCD ternary codes. We characterize right-symplectic ACD codes.

Authors

Sarra Manseri
Patrick Solé (ORCID: https://orcid.org/0000-0002-4078-8301)
Widyan Basaffar (ORCID: https://orcid.org/0000-0003-1639-9186)
Adel Alahmadi (ORCID: https://orcid.org/0000-0002-7758-3537)

Institutions

Centre National de la Recherche Scientifique (FR)
King Abdulaziz University (SA)
Central China Normal University (CN)
Centrale Méditerranée (FR)
Institut Polytechnique de Bordeaux (FR)

Publication Details

Journal: Entropy
Published: 2025-09-18
DOI: https://doi.org/10.3390/e27090973
Primary Topic: Coding theory and cryptography
Type: article
Field-Weighted Citation Impact: 0.00

Funders

King Abdulaziz University

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article

Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine

Sarra Manseri, Patrick Solé, Widyan Basaffar, Adel Alahmadi

Sep 18, 2025

Entropy

Coding theory and cryptography

article

Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine

Sarra Manseri, Patrick Solé, Widyan Basaffar, Adel Alahmadi

September 18, 2025article en

Abstract

We introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic-self-orthogonal and LCD ternary codes. We characterize right-symplectic ACD codes.

EntropyVol. 27(9)

Centre National de la Recherche Scientifique (FR), King Abdulaziz University (SA), Central China Normal University (CN), Centrale Méditerranée (FR), Institut Polytechnique de Bordeaux (FR)

King Abdulaziz University

Openalex Percentile: Top 87%

Coding theory and cryptography

DOI Open Access PDF OpenAlex

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Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine — Sarra Manseri, Patrick Solé, et al. · Entropy (2025) | TGRS Research Map | TGRS