Optimal Codes With Small Constant Weight in ℓ₁-Metric
| Autor: | Tingting Chen, Xiande Zhang, Yiming Ma |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Group (mathematics) 020206 networking & telecommunications Hamming distance 02 engineering and technology Library and Information Sciences Computer Science Applications Combinatorics Ternary Golay code Combinatorial design Metric (mathematics) 0202 electrical engineering electronic engineering information engineering Constant (mathematics) Ternary operation Information Systems |
| Zdroj: | IEEE Transactions on Information Theory. 67:4239-4254 |
| ISSN: | 1557-9654 0018-9448 |
| Popis: | Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in $\ell _{1}$ -metric. By using packings and group divisible designs in combinatorial design theory, we give constructions of optimal codes over non-negative integers and optimal ternary codes with $\ell _{1}$ -weight ${w}\leq 4$ for all possible distances. In general, we derive the size of the largest ternary code with constant weight $w$ and distance $2{w}-2$ for sufficiently large length n satisfying ${n}\equiv 1, {w},- {w}+2,-2{w}+3\pmod {{w}({w}-1)}$ . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|