Half-cyclic, dihedral and half-dihedral codes
Motivated by the study of a family of graphs introduced by \textit{C. E. Praeger} and \textit{M. Xu} [Eur. J. Comb. 10, No. 1, 91--102 (1989; Zbl 0672.05040)], the authors of the paper under review study linear codes in \(\mathbb{F}_2^n\) which are invariant under the actions of some subgroups of the dihedral group \(\mathbb{D}_n=\langle R,M\rangle\), where \(R\) is a cyclic rotation of the positions of the code and \(M\) reverses the codewords. So, they introduce the following terminologies: a code in \(\mathbb{F}_2^n\) is said half-cyclic/dihedral/half-dihedral if it is invariant under the action of \(\langle R^2\rangle\) / \(\langle R,M\rangle\) / \(\langle R^2,M\rangle\), respectively. In Theorem 2.11, the authors classify half-cyclic codes, in Theorem 3.3 they classify the dihedral codes and in Theorem 3.5 classify half-dihedral codes.
scientific article; zbMATH DE number 7435154
scientific article