Symplectic Hulls over a Non-Unital Ring

Anup Kushwaha; Om Prakash

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arXiv · 2601.06609

Symplectic Hulls over a Non-Unital Ring

Anup Kushwaha·Om Prakash

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Abstract

This paper presents the study of the symplectic hulls over a non-unital ring $ E= \langle \kappa,\tau \mid 2 \kappa =2 \tau=0,~ \kappa^2=\kappa,~ \tau^2=\tau,~ \kappa \tau=\kappa,~ \tau \kappa=\tau \rangle$. We first identify the residue and torsion codes of the left, right, and two-sided symplectic hulls, and characterize the generator matrix of the two-sided symplectic hull of a free $E$-linear code. Then, we explore the symplectic hull of the sum of two free $E$-linear codes. Subsequently, we provide two build-up techniques that extend a free $E$-linear code of smaller length and symplectic hull-rank to one of larger length and symplectic hull-rank. Further, for free $E$-linear codes, we discuss the permutation equivalence and investigate the symplectic hull-variation problem. An application of this study is given by classifying the free $E$-linear optimal codes for smaller lengths.

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Anup Kushwaha, Om Prakash. 2026-01-10. Symplectic Hulls over a Non-Unital Ring. https://arxiv.org/abs/2601.06609

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