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- W2962712345 abstract "Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An alternative algorithm for factorizing $x^n-lambda $ over ${mathbb{F}_{{q^2}}}$ is given, where $λ$ is a unit in ${mathbb{F}_{{q^2}}}$. Based on this factorization, the dimensions of the Hermitian hulls of $lambda $-constacyclic codes of length $n$ over ${mathbb{F}_{{q^2}}}$ are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dual) codes of length $n$ over ${mathbb{F}_{{q^2}}}$ are given through their Hermitian hulls. Subsequently, a new family of MDS constacyclic Hermitian self-dual codes over ${mathbb{F}_{{q^2}}}$ is introduced.As a generalization of constacyclic codes, quasi-twisted Hermitian self-dual codes are studied. Using the factorization of $x^n-lambda $ 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 ${mathbb{F}_{{q^2}}}$. 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." @default.
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- W2962712345 date "2017-01-01" @default.
- W2962712345 modified "2023-09-25" @default.
- W2962712345 title "Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields" @default.
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- W2962712345 doi "https://doi.org/10.3934/amc.2017045" @default.
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