论文信息 - A New Scheme to Determine the Weight Distributions of Binary Extended Quadratic Residue Codes

A New Scheme to Determine the Weight Distributions of Binary Extended Quadratic Residue Codes

This letter proposes a novel scheme which consists of a weight-counting algorithm, the combinatorial designs of the Assmus-Mattson theorem, and the weight polynomial of Gleason's theorem to determine the weight distributions of binary extended quadratic residue codes. As a consequence, the weight distributions of binary (138, 69, 22) and (168, 84, 24) extended quadratic residue codes are given.

Chong-Dao Lee | Trieu-Kien Truong | Yaotsu Chang | Wen-Ku Su

[1] Masaaki Harada,et al. Extremal binary self-dual codes , 1997, IEEE Trans. Inf. Theory.

[2] V. Pless. Introduction to the Theory of Error-Correcting Codes , 1991 .

[3] H. Mattson,et al. New 5-designs , 1969 .

[4] Vera Pless,et al. Introduction to the Theory of Error-Correcting Codes , 1991 .

[5] Alfred Wassermann,et al. On the weight enumerators of duadic and quadratic residue codes , 2004, IEEE Transactions on Information Theory.

[6] Jean-Marie Goethals. Analysis of weight distribution in binary cyclic codes (Corresp.) , 1966, IEEE Trans. Inf. Theory.

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

[8] Shirley Dex,et al. JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[9] Andrew M. Gleason,et al. WEIGHT POLYNOMIALS OF SELF-DUAL CODES AND THE MacWILLIAMS IDENTITIES , 1970 .

[10] Chong-Dao Lee,et al. The weight distributions of some binary quadratic residue codes , 2005, IEEE Transactions on Information Theory.

[11] Vera Pless,et al. Power Moment Identities on Weight Distributions in Error Correcting Codes , 1963, Inf. Control..

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

[13] N. J. A. Sloane,et al. An Upper Bound for Self-Dual Codes , 1973, Inf. Control..

[14] T. C. Hu,et al. Combinatorial algorithms , 1982 .

[15] J. Macwilliams. A theorem on the distribution of weights in a systematic code , 1963 .