Bounds for Codes by Semidefinite Programming

Details Bounds for Codes by Semidefinite Programming Bounds for Codes by Semidefinite Programming

2006-09-05

arxiv.org/abs/math/0609155v2

Proc. Steklov Inst. Math., 263 (2008), 134-149.

Mathematics

Combinatorics

20 pages

Scientific paper

Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that using as variables power sums of distances this problem can be considered as a finite semidefinite programming problem. This method allows to improve some linear programming upper bounds. In particular we obtain new bounds of one-sided kissing numbers.

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