New linear codes with few weights derived from Kloosterman sums

摘要

Linear codes with few weights have applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Heng and Yue (2016) [14] and Tan, Zhou, Tang and Helleseth (2017) [25], we extend Tan, Zhou, Tang and Helleseth's work to obtain a class of optimal 1-weight binary linear codes, new classes of 2-weight and 3-weight p-ary linear codes and a class of 4-weight binary linear codes. The lengths and weight distributions of the t-weight linear codes, where t = 1,2,3, are closed-form expressions of Kloosterman sums over finite prime fields, and are completely determined when p = 2 and P = 3. (C) 2019 Elsevier Inc. All rights reserved.