A Class of Linear Codes with a Few Weights

Abstract

Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of linear codes with a few weights over the finite field $\gf(p)$ are presented and their weight distributions are also determined, where $p$ is an odd prime. Some of the linear codes obtained are optimal in the sense that they meet certain bounds on linear codes.