On the Hulls of Group Codes

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 $\le 3$. In particular our criterion for the existence of $1$-dimensional hulls generalizes that of privious work which consider only abelian groups $G$.

Submitted to Designs, Codes and Cryptography. Submission ID 64937899-ea28-4559-9d88-9de59566a860