| Numerical Results on the Asymptotic Rate of Binary Codes (2007) | |||||||||||||||
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| . We compute upper bounds on the maximal size of a binary linear code of length n 1000, dimension k, and distance d For each value of d, the bound is found by solving the Delsarte linear programming problem. Relying on the results of the calculations, we discuss the known bounds on the size of codes and some recent conjectures made about them. The most important conclusion is that Delsarte's linear programming method is unlikely to yield major improvements of the known general upper bounds on the size of codes. 1. Introduction: bounds on codes A codeC is a subset of the binary Hamming space H n 2 . The minimum distance between a pair of distinct points in C is called the distance of C, denoted d C One of the main problems of coding theory is to find the maximal size A n d of a code with given distance d. This problem is solved exactly only for some small values of n and d. The general results known are in the form of upper and lower bounds. The aim of this paper is to explore the l... | |||||||||||||||
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