LCD codes and self-orthogonal codes in generalized dihedral group algebras.

Let F q be a finite field with q elements, D 2 n , r a generalized dihedral group with gcd (2 n , q) = 1 , and F q [ D 2 n , r ] a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of F q [ D 2 n , r ] is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in F q [ D 2 n , r ] are precisely described and counted. Some numerical examples are also presented to illustrate our main results. [ABSTRACT FROM AUTHOR]