2021/03/19 by Liqin Qian, Qian, Liqin, Xiwang Cao +6
Computer Science · Engineering · Mathematics · #Algorithm #Block code #Circulant matrix #Code (set theory) #Coding theory and cryptography #Combinatorics #Computer science #Cooperative Communication and Network Coding #Discrete mathematics #Dual (grammatical number) #Dual code #Engineering #Error Correcting Code Techniques #FOS: Computer and information sciences #Hull #Information Theory (cs.IT) #Intersection (aeronautics) #Linear code #Mathematics #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.2103.10874
arxiv created 2021/03/19 · openalex publication_date 2021/03/19 · arxiv updated 2021/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hull of a linear code over finite fields is the intersection of the code and its dual, which was introduced by Assmus and Key. In this paper, we develop a method to construct linear codes with trivial hull ( LCD codes) and one-dimensional hull by employing the positive characteristic analogues of Gauss sums. These codes are quasi-abelian, and sometimes doubly circulant. Some sufficient conditions for a linear code to be an LCD code (resp. a linear code with one-dimensional hull) are presented. It is worth mentioning that we present a lower bound on the minimum distances of the constructed linear codes. As an application, using these conditions, we obtain some optimal or almost optimal LCD codes (resp. linear codes with one-dimensional hull) with respect to the online Database of Grassl.