Self-Orthogonal Codes from Vectorial Dual-Bent Functions

Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In {HLL2023Te,LH2023Se}, p-ary self-orthogonal codes were constructed by using p-ary weakly regular bent functions, where p is an odd prime. In {WH2023Se}, two classes of non-degenerate quadratic forms were used to construct q-ary self-orthogonal codes, where q is a power of a prime. In this paper, we construct new families of q-ary self-orthogonal codes using vectorial dual-bent functions. Some classes of at least almost optimal linear codes are obtained from the dual codes of the constructed self-orthogonal codes. In some cases, we completely determine the weight distributions of the constructed self-orthogonal codes. From the view of vectorial dual-bent functions, we illustrate that the works on constructing self-orthogonal codes from p-ary weakly regular bent functions {HLL2023Te,LH2023Se} and non-degenerate quadratic forms with q being odd {WH2023Se} can be obtained by our results. We partially answer an open problem on determining the weight distribution of a class of self-orthogonal codes given in {LH2023Se}. As applications, we construct new infinite families of at least almost optimal q-ary linear complementary dual codes (for short, LCD codes) and quantum codes.