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This is a Quantitative Study study.

September 20, 2025EntropyOpen Access

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

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The study introduces quasi self-dual, linear complementary dual, and additive complementary dual codes.
These codes are analyzed over a non-commutative non-unitary ring of order 9, establishing new connections.
The characterization of right-symplectic ACD codes provides insights into their structural properties.
Connections to symplectic–self-orthogonal and LCD ternary codes reinforce the relevance of these codes.

Implication

This research introduces QSD and ACD codes over non-commutative rings, highlighting their symplectic properties.

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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Cite This Study

Manseri et al. (2025) studied this question.

synapsesocial.com/papers/68d469ce31b076d99fa66b22 https://doi.org/10.3390/e27090973

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Implication

This research introduces QSD and ACD codes over non-commutative rings, highlighting their symplectic properties.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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