Constructions of linear codes with small hulls from association schemes
Ye Wang, Ran Tao · Advances in Mathematics of Communications · 2020
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.