New Upper Bounds on A(n,d)
Beniamin Mounits (1), Tuvi Etzion (1), Simon Litsyn (2) ((1), Technion - Israel Institute of Technology, (2) Tel Aviv University)
TL;DR
This paper introduces new upper bounds on the maximum size of binary codes with specified length and minimum Hamming distance, using linear programming and counting methods, leading to improved bounds for small code lengths.
Contribution
It presents novel upper bounds that improve existing analytic bounds and establishes new record bounds for small-length codes.
Findings
Improved upper bounds on binary codes.
New record bounds for small code lengths.
Enhanced methods combining linear programming and counting.
Abstract
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds improve on the best known analytic bounds. Several new record bounds are obtained for codes with small lengths.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Advanced Wireless Communication Techniques