Constacyclic and quasi-twisted hermitian self-dual codes over finite fields

Abstract

Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An alternative algorithm for factorizing xn − λ over Fq2 is given, where λ is a unit in Fq2. Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over Fq2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dual) codes of length n over Fq2 are given through their Hermitian hulls. Subsequently, a new family of MDS constacyclic Hermitian self-dual codes over Fq2 is introduced. As a generalization of constacyclic codes, quasi-twisted Hermitian self-dual codes are studied. Using the factorization of xn − λ and the Chinese Remainder Theorem, quasi-twisted codes can be viewed as a product of linear codes of shorter length over some extension fields of Fq2. Necessary and sufficient conditions for quasi-twisted codes to be Hermitian self-dual are given. The enumeration of such self-dual codes is determined as well.