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Complementary Dual Subfield Linear Codes Over Finite Fields (1605.06827v1)

Published 22 May 2016 in cs.IT and math.IT

Abstract: Two families of complementary codes over finite fields $\mathbb{F}_q$ are studied, where $q=r2$ is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and sufficient conditions for a linear code (resp., a subfield linear code) to be Hermitian complementary dual (resp., trace Hermitian complementary dual) are determined. Constructions of such codes are given together their parameters. Some illustrative examples are provided as well.

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