The weight distribution of a class of two-weight linear codes derived from Kloosterman sums

Abstract

Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, a class of p-ary two-weight linear codes is constructed using a generic construction developed by Ding et al. recently, where p is a prime. Their length and weight distribution are closed-form expressions of Kloosterman sums over prime finite fields, and are completely determined when p = 2 and p = 3. The dual of this class of linear codes is also studied and is shown to be optimal or almost optimal in the binary case.