Symbol-pair weight distribution of some irreducible cyclic codes (Q6159438)

In the last decade, a relationship between the minimum Hamming distance of an error-correcting code and the minimum pair distance was established and investigated by many researchers. In this paper, the authors study the symbol-pair weight distribution of some irreducible cyclic codes. They define generalized cyclotomic numbers and provide some of their properties. Using a special kind of sum, they establish a relationship among the symbol-pair weight of irreducible cyclic codes, generalized cyclotomic numbers and the Gaussian periods. Moreover, they determine the symbol-pair weight distribution of some classes of irreducible cyclic codes.