Complete weight enumerators of some linear codes and their applications

Abstract

Recently, linear codes constructed from defining sets have been extensively studied. It was shown that the linear codes may have a few nonzero weights or be optimal if the defining sets are well chosen. The weight enumerators of these linear codes were also presented. In this paper, we investigate the complete weight enumerators of some linear codes constructed from the defining sets. As applications, we employ the explicit complete weight enumerators of the linear codes to construct constant composition codes and systematic authentication codes. A new class of optimal constant composition codes and three classes of asymptotically optimal systematic authentication codes are presented