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Complete weight enumerators of a class of linear codes with two weights

Authors:	Guangkui Xu Xiwang Cao Shanding Xu Jingshui Ping

Institution:	1. Department of Applied Mathematics, Huainan Normal University, Huainan 232038, China;2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;4. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 210016, China

Abstract:	In this paper, a class of $p$ -ary linear codes with two weights is constructed by using the properties of cyclotomic classes of $F_{p^{2}}^{1}$ . The complete weight enumerators of these linear codes are also determined. In some cases, they are optimal and can be employed to obtain secret sharing schemes with interesting access structures and asymptotically optimal systematic authentication codes.

Keywords:	Complete weight enumerators Linear codes Authentication codes Secret sharing schemes
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