LCD and Self-Orthogonal Group Codes in a Finite Abelian $p$ -Group Algebra
Fengwei Li, Qin Yue, Yansheng Wu · IEEE Transactions on Information Theory · 2019
Let Fqbe a finite field with q elements and p be a prime with gcd(p, q) = 1. Let G be a finite abelian p-group and Fq(G) be a group algebra. In this paper, we find all primitive idempotents and minimal abelian group codes in the group algebra Fq(G). Furthermore, we give all LCD abelian codes (linear code with complementary dual) and self-orthogonal abelian codes of Fq(G).