Weight Distributions of a Class of Linear Codes*

Linear codes with a few weights have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs, and they are also of importance in consumer electronics, communications and data storage systems. In this literature, based on the theory of defining sets, we present a class of five-weight linear codes over $\mathbb{F}_p$ (p is an odd prime). Then, we use exponential sums to determine its weight distributions.

[1]  Dongmei Huang,et al.  Two-Weight and Three-Weight Linear Codes From Square Functions , 2016, IEEE Communications Letters.

[2]  Qin Yue,et al.  Complete weight distributions of two classes of cyclic codes , 2017, Cryptography and Communications.

[3]  W. Cary Huffman,et al.  Fundamentals of Error-Correcting Codes , 1975 .

[4]  Keqin Feng,et al.  On the Weight Distributions of Two Classes of Cyclic Codes , 2008, IEEE Transactions on Information Theory.

[5]  Li Chao.  Construction of A Class of Linear Codes with Good Parameters , 2003 .

[6]  Cunsheng Ding,et al.  Cyclotomic Linear Codes of Order $3$ , 2007, IEEE Transactions on Information Theory.

[7]  Dongdai Lin,et al.  Complete weight enumerators of a class of three-weight linear codes , 2017 .

[8]  Cunsheng Ding,et al.  A Generic Construction of Cartesian Authentication Codes , 2007, IEEE Transactions on Information Theory.

[9]  A. Calderbank,et al.  THREE-WEIGHT CODES AND ASSOCIATION SCHEMES , 2014 .

[10]  Robert J. McEliece,et al.  Weights of Irreducible Cyclic Codes , 1972, Inf. Control..

[11]  R. Calderbank,et al.  The Geometry of Two‐Weight Codes , 1986 .

[12]  Robert S. Coulter.  Further evaluations of Weil sums , 1998 .

[13]  Cunsheng Ding,et al.  Secret sharing schemes from three classes of linear codes , 2006, IEEE Transactions on Information Theory.

[14]  Tor Helleseth,et al.  The weight distribution of a class of two-weight linear codes derived from Kloosterman sums , 2018, Cryptography and Communications.