A construction of several classes of two-weight and three-weight linear codes

摘要

Linear codes constructed from defining sets have been extensively studied and may have a few nonzero weights if the defining sets are well chosen. Let be a finite field with elements, where p is a prime and m is a positive integer. Motivated by Ding and Ding's recent work (IEEE Trans Inf Theory 61(11):5835-5842, 2015), we construct p-ary linear codes by where and is the trace function from onto . In this paper, we will employ exponential sums to investigate the weight enumerators of the linear codes , where for two positive integers and . Several classes of two-weight and three-weight linear codes and their explicit weight enumerators are presented if . By deleting some coordinates, more punctured two-weight and three-weight linear codes which include some optimal codes are derived from C-D.