Abstract
Let Fq be a finite field with order q, Q4n the generalized quaternion group with 4n elements, and gcd(4n,q)=1. Firstly, central (right) irreducible idempotents of Fq[Q4n] are determined in two cases: q≡1(mod4) and q≡3(mod4). Secondly, precise descriptions and enumerations of linear complementary dual (LCD) codes and self-orthogonal codes in the generalized quaternion group algebras Fq[Q4n] are obtained. Some numerical examples are also presented to illustrate our applications.
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