On the Hulls of Group Codes

2025/07/29 by Deng, Xiheng, Ren, Yuan
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2507.21623

Abstract

Let \mathbb F_q be a finite field and G a finte group with (|G|,q)=1. By a group code in \mathbb F_q[G] we mean a two-sided ideal in \mathbb F_q[G]. We will prove a general criterion for the existence of group codes with given hull dimension, and then apply it to deduce explicit criterions for existence of group codes with hull dimension ≤3. In particular our criterion for the existence of 1-dimensional hulls generalizes that of privious work which consider only abelian groups G.

Citations

• On linear codes with one-dimensional Euclidean hull and their applications to EAQECCs
• Good Quantum Error-Correcting Codes Exist

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