2011-№4(33) Article 16
B. Mounits
New upper bounds for nonbinary codes. р. 189-201
UDC 53
The paper presents new upper bounds for non-binary codes. The bounds can be obtained by linear and semidefinite programming.
bounds, codes, programming.
References
1. Bannai, E. Algebraic Combinatorics I: Association Schemes, Benjamin/ E. Bannai, T. Ito. – Cummings, Menlo Park, ca, 1984.
2. Delsarte, Ph. Bounds for unrestricted codes, by linear programming// Philips Res. Reports. – Vol. 27. – 1972, June. – P. 272–289.
3. Delsarte, Ph. An algebraic approach to the association schemes of coding theory// Philips Res. Reports Supplements.– 1973. – No. 10.
4. Gijswijt, D. New upper bounds for nonbiliary codes based on the Terwilliger algebraand semidefinite programming [Text]/ D. Gijswijt, A. Schrijver, H. Tanaka// Journal ofComb. Theory, Ser. A. – Vol. 113. – 2006. – P. 1719–1731/
5. MacWilliams, F.J. The Theory of Error-Correcting Codes/ F.J. MacWilliams, N.J. A. Sloane. – Amsterdam: North-Holland, 1977.
6. Mounits, B. Upper Bounds on Codes via Association Schemes and Linear Programming/ B. Mounits, T. Etzion, S. Litsyn. – Advances in Mathematics, of Communications.
7. Schrijver, A. New code upper bounds from the Terwilliger algebra and semidefiniteprogramming [Text]// IEEE Trans, on Inform. Theory. – Vol. 51. – 2005, Aug. – P. 2859–2866.