IIM  Vol.2 No.3 , March 2010
Lexicographic Constant-Weight Equidistant Codes over the Alphabet of Three, Four and Five Elements
ABSTRACT
In this paper we consider the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements with 2 ≤ w < n ≤ 10. Computer search of lexicographic constant-weight equidistant codes is performed. Tables with bounds on the size of lexicographic constant-weight equidistant codes are presented.

Cite this paper
nullT. Todorov, G. Bogdanova and T. Yorgova, "Lexicographic Constant-Weight Equidistant Codes over the Alphabet of Three, Four and Five Elements," Intelligent Information Management, Vol. 2 No. 3, 2010, pp. 183-187. doi: 10.4236/iim.2012.23021.
References
[1]   C. J. Colbourn and J. H. Dinitz, “The CRC handbook of combinatorial designs,” Boca Raton, CRC Press, FL, 1996.

[2]   J. I. Hall, “Bounds for equidistant codes and partial projective planes,” Discrete Mathematics, Vol. 17, pp. 85–94, 1977.

[3]   J. I. Hall, A. J. E. M. Jansen, A.W. J. Kolen, and J. H. van Lint, “Equidistant codes with distance 12,” Discrete Mathematics, Vol. 17, pp. 71–83, 1977.

[4]   J. H. van Lint, “A theorem on equidistant codes,” Discrete Mathematics, Vol. 67, pp. 353–358, 1973.

[5]   N. V. Semakov and V. A. Zinoviev, “Equidistant q-ary codes with maximal distance and resolvable balanced incomplete block designs,” Problemi peredachi Informatsii, Vol. 4, No. 2, pp. 3–10, 1968.

[6]   A. E. Brouwer, J. B. Shearer, N. J. A. Sloane, and W. D. Smith, “A new table of constant-weight codes,” IEEE Transactions on Information Theory, Vol. 36, pp. 1344– 1380, 1990.

[7]   E. Agrell, A. Vardy, and K. Zeger, “Upper bounds for constant-weight codes,” IEEE Transactions on Information and Theory, Vol. IT-46, pp. 2373–2395, 2000.

[8]   G. T. Bogdanova, “New bounds for the maximum size of ternary constant weight codes,” Serdica Mathematics Journal, Vol. 26, pp. 5–12, 2000.

[9]   M. Svanstr?m, P. R. J. ?sterg?rd, and G. T. Bogdanova, “Bounds and constructions for ternary constant-composition codes,” IEEE Transactions on Information Theory, Vol. 48, No. 1, pp. 101–111, 2002.

[10]   D. R. Stinson and G. H. J. van Rees, “The equivalence of certain equidistant binary codes and symmetric BIBDs,” Combinatorica, Vol. 4, pp. 357–362, 1984.

[11]   F. W. Fu, T. Klove, Y. Luo, and V. K. Wei., “On equidistant constant weight codes,” In Proceedings WCC’2001 Workshop on Coding and Cryptography, Paris, France, pp. 225–232, January 2001.

[12]   J. H. Conway, “Integral lexicographic codes,” Discrete Mathematics, Vol. 83, pp. 219–235, 1990.

[13]   J. H. Conway and N. J. A. Sloane, “Lexicographic codes: Error-correcting codes from game theory,” IEEE Transactions on Information Theory, Vol. 32, pp. 337–348, 1986.

[14]   R. A. Brualdi and V. S. Pless, “Greedy codes,” Journal of Combinatorial Theory (A), September 1993.

[15]   M. Plotkin, “Binary codes with specified minimum distance,” IRE Transactions on Information Theory, Vol. 6, pp. 445–450, 1960.

[16]   P. Delsarte, “Bounds for unrestricted codes, by linear programming,” Philips Research, Vol. 27, pp. 47–64, 1972.

[17]   G. Bogdanova, T. Todorov, and T. Pagkou, “New equidistant constant weight codes over the alphabet of three, four and five elements,” Preprint №1/2008, BAS, 2008.

[18]   G. Bogdanova, T. Todorov, and V. Zinoviev, “On construction of q-ary equidistant codes,” Problems of Information Transmission, Vol. 43, pp. 13–36, 2007.

[19]   G. Bogdanova, T. Todorov, and V. Todorov, “Web-based application for coding theory studying,” In Proceedings of the International Congress of Mathematical Society of Southeastern Europe, Borovets, Bulgaria, pp. 94–99, Sep- tember 15–21, 2003.

 
 
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