Constructions of linear codes with small hulls from association schemes | Zendy

Ye Wang | Zendy; Ran Tao | Zendy

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Constructions of linear codes with small hulls from association schemes

Author(s) -

Ye Wang,

Ran Tao

Publication year - 2020

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.

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