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Linear Size Constant-Composition Codes Meeting the Johnson Bound.
- Source :
- IEEE Transactions on Information Theory; Feb2018, Vol. 64 Issue 2, p909-917, 9p
- Publication Year :
- 2018
-
Abstract
- The Johnson-type upper bound on the maximum size of a code of length n , distance d=2w-1 , and constant composition \overline w is \lfloor \dfrac \vphantom R^.nw1\rfloor , where w is the total weight and w_{1} is the largest component of {\overline {w}} . Recently, Chee et al. proved that this upper bound can be achieved for all constant-composition codes of sufficiently large lengths. Let Nccc({\overline {w}}) be the smallest such length. The determination of Nccc({\overline {w}}) is trivial for binary codes. This paper provides a lower bound on Nccc({\overline {w}}) , which is shown to be tight for all ternary and quaternary codes by giving new combinatorial constructions. Consequently, by the refining method, we determine the values of Nccc({\overline {w}}) , for all $q$ -ary constant-composition codes, provided that 3w_{1}\geq w with finite possible exceptions. [ABSTRACT FROM AUTHOR]
- Subjects :
- BINARY codes
CODING theory
BINARY sequences
MATHEMATICS education
CIPHERS
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 64
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 127408965
- Full Text :
- https://doi.org/10.1109/TIT.2017.2689026