16 research outputs found
One-Generator Quasi-Abelian Codes Revisited
The class of 1-generator quasi-abelian codes over finite fields is revisited.
Alternative and explicit characterization and enumeration of such codes are
given. An algorithm to find all 1-generator quasi-abelian codes is provided.
Two 1-generator quasi-abelian codes whose minimum distances are improved from
Grassl's online table are presented
One–generator quasi–abelian codes revisited
The class of 1-generator quasi-abelian codes over finite fields is revisited. Alternative and explicit characterization and enumeration of such codes are given. An algorithm to find all 1-generator quasi-abelian codes is provided. Two 1-generator quasi-abelian codes whose minimum distances are improved from Grassl’s online table are presented
Hermitian self-dual quasi-abelian codes
Quasi-abelian codes constitute an important class of linear codes containing theoretically and practically interesting codes such as quasi-cyclic codes, abelian codes, and cyclic codes. In particular, the sub-class consisting of 1-generator quasi-abelian codes contains large families of good codes. Based on the well-known decomposition of quasi-abelian codes, the characterization and enumeration of Hermitian self-dual quasi-abelian codes are given. In the case of 1-generator quasi-abelian codes, we offer necessary and sufficient conditions for such codes to be Hermitian self-dual and give a formula for the number of these codes. In the case where the underlying groups are some -groups, the actual number of resulting Hermitian self-dual quasi-abelian codes are determined