Constructions of Self-Orthogonal Codes and LCD Codes Over Finite Fields

Self-orthogonal codes, which are contained within their dual codes, have applications in linear complementary dual codes, quantum codes, etc. In this paper, we generalize the construction method given by Heng et al. in [Des. Codes Cryptogr. 91(12), 2023] to weakly regular plateaued functions. We first construct several families of p-ary self-orthogonal linear codes with few weights from weakly regular plateaued balanced and unbalanced functions over the finite fields of odd characteristics. Then, we use the constructed p-ary self-orthogonal codes to build new families of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex>-arv LCD codes.