Bounds for codes by semidefinite programming
نویسندگان
چکیده
منابع مشابه
Bounds for Codes by Semidefinite Programming
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 l...
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We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras. The Delsarte ...
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The paper describes a problem of linear programming associated with distance properties of unrestricted codes. As a solution to the problem, one obtains an .upper bound for the number of words in codes having a prescribed set of distances. 1. Introduetion Important information about a code is contained in its Hamming distance distribution, defined as follows: for a q-ary code C of length n, it ...
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ژورنال
عنوان ژورنال: Proceedings of the Steklov Institute of Mathematics
سال: 2008
ISSN: 0081-5438,1531-8605
DOI: 10.1134/s0081543808040111