Linear Codes with Two or Three Weights From Quadratic Bent Functions

Abstract

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field $\gf_p$, where $p$ is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined.