Constructing error-correcting binary codes using transitive permutation groups
作者： Patric R. J. Östergård , Antti Laaksonen
DOI:
关键词: Minimum distance 、 Permutation group 、 Computer search 、 Transitive relation 、 Discrete mathematics 、 Combinatorics 、 Mathematics 、 Error correcting 、 Binary code 、 Maximum size
摘要: Let $A_2(n,d)$ be the maximum size of a binary code length $n$ and minimum distance $d$. In this paper we present following new lower bounds: $A_2(18,4) \ge 5632$, $A_2(21,4) 40960$, $A_2(22,4) 81920$, $A_2(23,4) 163840$, $A_2(24,4) 327680$, $A_2(24,10) 136$, $A_2(25,6) 17920$. The bounds are result systematic computer search over transitive permutation groups.
arxiv.org参考文章(7)
Alexander Hulpke, Constructing transitive permutation groups Journal of Symbolic Computation. ,vol. 39, pp. 1- 30 ,(2005) , 10.1016/J.JSC.2004.08.002
John J. Cannon, Derek F. Holt, The Transitive Permutation Groups of Degree 32 Experimental Mathematics. ,vol. 17, pp. 307- 314 ,(2008) , 10.1080/10586458.2008.10129046
Beniamin Mounits, , Tuvi Etzion, Simon Litsyn, , , New upper bounds on codes via association schemes and linear programming Advances in Mathematics of Communications. ,vol. 1, pp. 173- 195 ,(2007) , 10.3934/AMC.2007.1.173
B. Mounits, T. Etzion, S. Litsyn, Improved upper bounds on sizes of codes IEEE Transactions on Information Theory. ,vol. 48, pp. 880- 886 ,(2002) , 10.1109/18.992776
PRJ Ostergard, Markku K Kaikkonen, None, New single-error-correcting codes IEEE Transactions on Information Theory. ,vol. 42, pp. 1261- 1262 ,(1996) , 10.1109/18.508854
M. Best, A. Brouwer, F. MacWilliams, A. Odlyzko, N. Sloane, Bounds for binary codes of length less than 25 IEEE Transactions on Information Theory. ,vol. 24, pp. 81- 93 ,(1978) , 10.1109/TIT.1978.1055827
Patric Östergård, Sampo Niskanen, Cliquer user's guide, version 1.0 ,(2003)