Constructing few-weight linear codes and strongly regular graphs (Q2675859)

Among the classes of linear codes, linear codes with few weights attracted more attention due to their easier implementation and deep connection to other fields or combinatorial objects, such as algebraic combinatorics, in particular strongly regular graphs [\textit{R. Calderbank} and \textit{W. M. Kantor}, Bull. Lond. Math. Soc. 18, 97--122 (1986; Zbl 0582.94019)]. How to construct linear codes with few weights is one important problem in the area of coding theory. In the paper under review, the authors construct a class of nine-weight linear codes by choosing defining sets from cyclotomic classes (Theorem 1). The authors also establish two-weight linear codes by employing weakly regular bent functions (Theorem 2). They obtain some codes that are minimal and also obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound (Theorem 3). Finally, the authors get a class of strongly regular graphs with new parameters by using the obtained two-weight linear codes (Theorem 4, Theorem 5, and Theorem 6).