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Optimal Quaternary Constant-Weight Codes With Weight Four and Distance Five.
- Source :
-
IEEE Transactions on Information Theory . Mar2013, Vol. 59 Issue 3, p1617-1629. 13p. - Publication Year :
- 2013
-
Abstract
- Constant-weight codes play an important role in coding theory. The problem of determining the sizes for optimal quaternary constant-weight codes with length n, weight 4, and minimum Hamming distance 5 ((n,5,4)4 codes) has been investigated in several papers. Although some constructions and several infinite families for such codes with length n\equiv 0,1\pmod4 have been given, the problem is still far from complete. In this paper, we determine the size of an optimal (n,5,4)4 code for each integer n\geq 4 leaving 55 lengths unsolved. Especially, for length n\equiv 0,1\pmod 4, the existence problem of the equivalent combinatorial object, namely the generalized Steiner system, is solved leaving only seven values undetermined. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CODING theory
*VECTORS (Calculus)
*MEDICAL care
*PROBLEM solving
*STEINER systems
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 59
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 85488131
- Full Text :
- https://doi.org/10.1109/TIT.2012.2227681