Constructions of cyclic quaternary constant-weight codes of weight three and distance four
| Autor: | Liantao Lan, Yanxun Chang, Lidong Wang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Code (set theory) Applied Mathematics Minimum distance 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Cyclic number (group theory) Computer Science Applications Combinatorics 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Constant-weight code Connection (algebraic framework) Constant (mathematics) Mathematics |
| Zdroj: | Designs, Codes and Cryptography. 86:1063-1083 |
| ISSN: | 1573-7586 0925-1022 |
| DOI: | 10.1007/s10623-017-0379-8 |
| Popis: | A cyclic $$(n,d,w)_q$$ code is a cyclic q-ary code of length n, constant-weight w and minimum distance d. A cyclic $$(n,d,w)_q$$ code with the largest possible number of codewords is said to be optimal. Optimal nonbinary cyclic $$(n,d,w)_q$$ codes were first studied in our recent paper (Lan et al. in IEEE Trans Inf Theory 62(11):6328–6341, 2016). In this paper, we continue to discuss the constructions of optimal cyclic $$(n,4,3)_q$$ codes. We establish the connection between cyclic $$(n,4,3)_{q}$$ codes and $$q-1$$ mutually orbit-disjoint cyclic (n, 3, 1) difference packings (briefly (n, 3, 1)-CDPs). For the case of $$q=4$$ , we construct three mutually orbit-disjoint (n, 3, 1)-CDPs by constructing a pair of strongly orbit-disjoint (n, 3, 1)-CDPs, which are obtained from Skolem-type sequences. As a consequence, we completely determine the number of codewords of an optimal cyclic $$(n,4,3)_{4}$$ code. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink