Weight Distributions of a Class of Linear Codes*

Abstract

Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this literature, based on the theory of defining sets, we present a class of five-weight linear codes over $\mathbb{F}_p$ (p is an odd prime). Then, we use exponential sums to determine its weight distributions.