
TL;DR
This paper establishes a general criterion for the existence of group codes with specified hull dimensions in group algebras over finite fields, extending previous results to non-abelian groups and small hull dimensions.
Contribution
It introduces a new criterion for the existence of group codes with given hull dimensions, applicable to non-abelian groups and small hull sizes, generalizing prior abelian-only results.
Findings
Criterion for existence of group codes with given hull dimension
Explicit conditions for hull dimension ≤ 3
Generalization to non-abelian groups
Abstract
Let be a finite field and a finte group with . By a group code in we mean a two-sided ideal in . 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 . In particular our criterion for the existence of -dimensional hulls generalizes that of privious work which consider only abelian groups .
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