Self-Orthogonal Codes from Vectorial Dual-Bent Functions
CoRR(2024)
Abstract
Self-orthogonal codes are a significant class of linear codes in coding
theory and have attracted a lot of attention. In ,
p-ary self-orthogonal codes were constructed by using p-ary weakly regular
bent functions, where p is an odd prime. In , 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
and non-degenerate quadratic forms with q being odd
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 . 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.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined