A Class of Nonbinary Codes and Their Weight Distribution

Nonlinear functions have important applications in coding theory and cryptography [16, 7]. Linear codes constructed from functions with high nonlinearity [17, 11, 2, 6] can be good and have useful applications in communications [9, 19, 10, 18] or cryptography [5, 4, 3, 21]. For a code, its weight distribution is important to study its structure and to provide information on the probability of undetected error when the code is used for error detection. Throughout this paper, let Fq be the finite field with q = p n elements for a prime p and a positive integer n, and let Fq be the multiplicative group of Fq. For an even integer n ≥ 4, let C k denote the [pn − 1, 5n/2] cyclic code given by Ck = {