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

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 18 Sep 2025 France English Publisher:MDPI AGJournal:Entropy, volume 27, page 973 (eissn: 1099-4300, Copyright policy )
Authors: Manseri, Sarra; Solé, Patrick; Alahmadi, Adel; Basaffar, Widyan;

doi: 10.3390/e27090973

pmid: 41008099

pmc: PMC12468440

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

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.

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Keywords

[MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], ACD codes, LCD codes, non-unitary ring, ternary codes, [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], symplectic QSD codes, Article

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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Average
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