Open AccessConstructions of linear codes with small hulls from association schemes
Author(s) -
Ye Wang,
Ran Tao
Publication year - 2022
Publication title -
advances in mathematics of communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.601
H-Index - 26
eISSN - 1930-5346
pISSN - 1930-5338
DOI - 10.3934/amc.2020114
Subject(s) - hull , mathematics , intersection (aeronautics) , dual (grammatical number) , dimension (graph theory) , code (set theory) , linear code , construct (python library) , dual code , linear span , discrete mathematics , arithmetic , block code , combinatorics , algorithm , computer science , programming language , engineering , art , decoding methods , literature , set (abstract data type) , marine engineering , aerospace engineering
The intersection of a linear code and its dual is called the hull of this code. The code is a linear complementary dual (LCD) code if the dimension of its hull is zero. In this paper, we develop a method to construct LCD codes and linear codes with one-dimensional hull by association schemes. One of constructions in this paper generalizes that of linear codes associated with Gauss periods given in [ 5 ]. In addition, we present a generalized construction of linear codes, which can provide more LCD codes and linear codes with one-dimensional hull. We also present some examples of LCD MDS, LCD almost MDS codes, and MDS, almost MDS codes with one-dimensional hull from our constructions.