Optimal cyclic quaternary constant-weight codes of weight three
| Autor: | Liantao Lan, Yanxun Chang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Code (set theory) Minimum distance Value (computer science) 020206 networking & telecommunications Q code 0102 computer and information sciences 02 engineering and technology 01 natural sciences Upper and lower bounds Combinatorics Distribution (mathematics) 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Constant (mathematics) Mathematics |
| Zdroj: | Journal of Combinatorial Designs. 26:174-192 |
| ISSN: | 1063-8539 |
| DOI: | 10.1002/jcd.21568 |
| Popis: | A cyclic (n,d,w)q code is a cyclic q-ary code of length n, constant weight w and minimum distance d. Let CAq(n,d,w) denote the largest possible size of a cyclic (n,d,w)q code. The pure and mixed difference method plays an important role in the determination of upper bound on CAq(n,d,w). By analyzing the distribution of odd mixed and pure differences, an improved upper bound on CA4(n,3,3) is obtained for n≡2,4(mod8). A new construction based on special sequences is provided and the exact value of CA4(n,d,3) is almost completely determined for all d and n except when d=3 and n≢18(mod24). Our constructions reveal intimate connections between cyclic constant weight codes and special sequences, particularly Skolem-type sequences. |
| Databáze: | OpenAIRE |
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