Existence and Construction of LCD codes over Finite Fields

08/16/2022

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by   Gyanendra K. Verma, et al.

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We demonstrate the existence of Euclidean and Hermitian LCD codes over finite fields with various parameters. In addition, we provide a method for constructing multiple Hermitian LCD (self orthogonal, self dual) codes from a given Hermitian LCD (self orthogonal, self dual) code, as well as a method for constructing Euclidean (Hermitian) LCD codes with parameters [n+1, k+1] and [n,k+1] from a given Euclidean (Hermitian) LCD code with parameters [n,k] over finite fields. Finally, we provide some findings on σ-LCD codes over finite fields.