The hulls of linear and cyclic codes have been extensively studied due to their wide applications. The dimensions and average dimension of the Euclidean hull of linear and cyclic codes have been well-studied. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length n over a finite field F q 2 is determined together with some upper and lower bounds. It turns out that either the average dimension of the Hermitian hull of constacyclic codes of length n over F q 2 is zero or it grows the same rate as n. Comparison to the average dimension of the Euclidean hull of cyclic codes is discussed as well.
Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing x n − λ over F q 2 is given, where λ is a unit in F q 2 . Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over F q 2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dual) codes of length n over F q 2 are given through their Hermitian hulls. Subsequently, a new family of MDS constacyclic Hermitian self-dual codes over F q 2 is introduced.As a generalization of constacyclic codes, quasi-twisted Hermitian self-dual codes are studied. Using the factorization of x n − λ and the Chinese Remainder Theorem, quasi-twisted codes can be viewed as a product of linear codes of shorter length some over extension fields of F q 2 . 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.
The hulls of linear and cyclic codes have been extensively studied due to their wide applications. The dimensions and average dimension of the Euclidean hull of linear and cyclic codes have been well-studied. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length n over a finite field F q 2 is determined together with some upper and lower bounds. It turns out that either the average dimension of the Hermitian hull of constacyclic codes of length n over F q 2 is zero or it grows the same rate as n. Comparison to the average dimension of the Euclidean hull of cyclic codes is discussed as well.
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