Weighted external difference families and R-optimal AMD codes
Combinatorics
2018-05-04 v1
Abstract
In this paper, we provide a mathematical framework for characterizing AMD codes that are R-optimal. We introduce a new combinatorial object, the reciprocally-weighted external difference family (RWEDF), which corresponds precisely to an R-optimal weak AMD code. This definition subsumes known examples of existing optimal codes, and also encompasses combinatorial objects not covered by previous definitions in the literature. By developing structural group-theoretic characterizations, we exhibit infinite families of new RWEDFs, and new construction methods for known objects such as near-complete EDFs. Examples of RWEDFs in non-abelian groups are also discussed.
Keywords
Cite
@article{arxiv.1805.01330,
title = {Weighted external difference families and R-optimal AMD codes},
author = {Sophie Huczynska and Maura B. Paterson},
journal= {arXiv preprint arXiv:1805.01330},
year = {2018}
}