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Improved upper bounds on sizes of codes
- Source :
- IEEE Transactions on Information Theory. April, 2002, Vol. 48 Issue 4, p880, 7 p.
- Publication Year :
- 2002
-
Abstract
- Let A(n, d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound. For small values of n and d, the best known method to obtain upper bounds on A(n, d) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on A(n, d) for n [less than or equal to] 28 are improved. Index Terms--A(n, d), holes, Johnson bound, linear programming bound.
- Subjects :
- Codes -- Analysis
Binary-coded notation -- Evaluation
Linear programming -- Usage
Subjects
Details
- ISSN :
- 00189448
- Volume :
- 48
- Issue :
- 4
- Database :
- Gale General OneFile
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- edsgcl.84866857