Optimal Ternary Codes with Weight $w$ and Distance $2w-2$ in $\ell_1$-Metric

Xin Wei; Tingting Chen; Xiande Zhang

Optimal Ternary Codes with Weight $w$ and Distance $2w-2$ in $\ell_1$-Metric

Combinatorics 2020-11-11 v1

Authors: Xin Wei , Tingting Chen , Xiande Zhang

Abstract

The study of constant-weight codes in $\ell_1$ -metric was motivated by the duplication-correcting problem for data storage in live DNA. It is interesting to determine the maximum size of a code given the length $n$ , weight $w$ , minimum distance $d$ and the alphabet size $q$ . In this paper, based on graph decompositions, we determine the maximum size of ternary codes with constant weight $w$ and distance $2w-2$ for all sufficiently large length $n$ . Previously, this was known only for a very sparse family $n$ of density $4/w(w-1)$ .

Keywords

constant-weight codes l1-metric ternary codes graph decomposition maximum size dna storage

Cite

@article{arxiv.2011.04932,
  title  = {Optimal Ternary Codes with Weight $w$ and Distance $2w-2$ in $\ell_1$-Metric},
  author = {Xin Wei and Tingting Chen and Xiande Zhang},
  journal= {arXiv preprint arXiv:2011.04932},
  year   = {2020}
}

Comments

13 pages, 1 figure

Optimal Ternary Codes with Weight $w$ and Distance $2w-2$ in $\ell_1$-Metric

Abstract

Keywords

Cite

Comments

Related papers