Four classes of linear codes from cyclotomic cosets (Q1744014)

The study of weight enumerators of linear codes is important for many goals -- it gives the error correcting ability of a given codes but also allows the computation of the probability of error detection and correction. In this paper the authors give four classes of linear codes from coset representatives of subgroups and cyclotomic coset families of some finite fields. By some combinatorial techniques and Gauss sums they compute the weight enumerators of these linear codes.