Constructions of Self-Orthogonal Linear Codes and Dual-Containing BCH Codes

Abstract

Self-orthogonal and dual-containing codes are two important subclasses of linear codes in coding theory and have been studied for many years. In this paper, we present several sufficient conditions for self-orthogonal or dual-containing codes when a linear code, cyclic code or BCH code $\mathcal {C}$ is transformed to an equivalent code ${\mathbf { v}} \cdot {\mathcal {C}}$ . Specifically, we prove that linear codes are equivalent to Euclidean or Hermitian self-orthogonal codes if the dimension is very small. For primitive BCH codes, we prove that when designed distances are small, equivalent Euclidean dual-containing codes always exist. From our method presented in this paper, many self-orthogonal or dual-containing linear, cyclic or BCH codes with good parameters can be constructed explicitly. We also construct some Euclidean dual-containing binary BCH codes with best-known parameters.