Optimal codes with small constant weight in $\ell_1$-metric
Information Theory
2020-10-12 v2 math.IT
Abstract
Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in -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 -weight for all possible distances. In general, we derive the size of the largest ternary code with constant weight and distance for sufficiently large length satisfying .
Cite
@article{arxiv.2003.00483,
title = {Optimal codes with small constant weight in $\ell_1$-metric},
author = {Tingting Chen and Yiming Ma and Xiande Zhang},
journal= {arXiv preprint arXiv:2003.00483},
year = {2020}
}