Binary Constant Weight Codes Based on Cyclic Difference Sets

Based on cyclic difference sets, sequences with two-valued autocorrelation can be constructed. Using these constructed sequences, two classes of binary constant weight codes are presented. Some codes proposed in this paper are proven to be optimal.

[1]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[2]  Fanxin Zeng.  Properties of m-Sequence and Construction of Constant Weight Codes , 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[3]  A. J. Han Vinck,et al.  On the Constructions of Constant-Weight Codes , 1998, IEEE Trans. Inf. Theory.

[4]  S.W. Golomb,et al.  Periodic binary sequences with the "trinomial property" , 1997, Proceedings of IEEE International Symposium on Information Theory.

[5]  László Györfi,et al.  Constructions of binary constant-weight cyclic codes and cyclically permutable codes , 1992, IEEE Trans. Inf. Theory.

[6]  Yeow Meng Chee,et al.  Constructions for $q$-Ary Constant-Weight Codes , 2007, IEEE Transactions on Information Theory.

[7]  Jie Ling,et al.  A construction of binary constant-weight codes from algebraic curves over finite fields , 2005, IEEE Transactions on Information Theory.

[8]  Alexander Vardy,et al.  Upper bounds for constant-weight codes , 2000, IEEE Trans. Inf. Theory.

[9]  Selmer M. Johnson.  A new upper bound for error-correcting codes , 1962, IRE Trans. Inf. Theory.

[10]  Victor Zinoviev,et al.  On binary cyclic codes with codewords of weight three and binary sequences with the trinomial property , 2001, IEEE Trans. Inf. Theory.

[11]  L. D. Baumert.  Cyclic Difference Sets , 1971 .