Complete weight enumerators of some linear codes from quadratic forms

Abstract

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q-ary linear codes with few weights employing general quadratic forms over the finite field Fq${\mathbb {F}}_{q}$ is proposed, where q is an odd prime power. This generalizes some earlier constructions of p-ary linear codes from quadratic bent functions over the prime field Fp${\mathbb {F}}_{p}$, where p is an odd prime. The complete weight enumerators of the resultant q-ary linear codes are also determined.