Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.7

The Number of Inequivalent (2R+3,7)R Optimal Covering Codes

Gerzson Kéri
Computer and Automation Research Institute
Hungarian Academy of Sciences
Kende u. 13-17
H-1111 Budapest
Hungary

Patric R. J. Östergård
Department of Electrical and Communications Engineering
Helsinki University of Technology
P. O. Box 3000
02015 TKK
Finland

Abstract: Let (n,M)R denote any binary code with length n, cardinality M and covering radius R. The classification of (2R+3,7)R codes is settled for any R=1,2,..., and a characterization of these (optimal) codes is obtained. It is shown that, for R=1,2,..., the numbers of inequivalent (2R+3,7)R codes form the sequence 1,3,8,17,33,... identified as A002625 in the Encyclopedia of Integer Sequences and given by the coefficients in the expansion of 1/((1-x)³(1-x²)²(1-x³)).

(Concerned with sequences A001399 A001400 A001401 A002625 A002625 and A072921 .)

Received January 11 2006; revised version received September 22 2006. Published in Journal of Integer Sequences September 22 2006.