Cyclic Constant-Weight Codes: Upper Bounds and New Optimal Constructions
| Autor: | Yanxun Chang, Lidong Wang, Liantao Lan |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Code (set theory) Minimum distance 020206 networking & telecommunications Hamming distance 0102 computer and information sciences 02 engineering and technology Library and Information Sciences 01 natural sciences Upper and lower bounds Electronic mail Computer Science Applications Combinatorics Mathematics::K-Theory and Homology 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Constant (mathematics) Information Systems Mathematics |
| Zdroj: | IEEE Transactions on Information Theory. 62:6328-6341 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2016.2613120 |
| Popis: | In this paper, we consider optimal $q$ -ary cyclic constant-weight codes of length $n$ , minimum distance $d$ , and weight $w$ , briefly cyclic $(n,d,w)_{q}$ codes. We introduce the pure and mixed difference method to present a combinatorial description for a cyclic $(n,d,w)_{q}$ code and then obtain some tight upper bounds on the sizes of optimal cyclic $(n,d,w)_{q}$ codes. Finally, by using Skolem-type sequences, we completely determine the sizes of optimal cyclic $(n,d,3)_{3}$ codes with minimum distance $1\leq d\leq 6$ . |
| Databáze: | OpenAIRE |
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