Weighted external difference families and R-optimal AMD codes

Huczynska, Sophie; Paterson, Maura

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Date

03/2019

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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.

Citation

Huczynska , S & Paterson , M 2019 , ' Weighted external difference families and R-optimal AMD codes ' , Discrete Mathematics , vol. 342 , no. 3 , pp. 855-867 . https://doi.org/10.1016/j.disc.2018.11.009

Publication

Discrete Mathematics

Status

Peer reviewed

DOI

https://doi.org/10.1016/j.disc.2018.11.009

ISSN

0012-365X

Type

Journal article

Rights

Copyright © 2018 Elsevier B.V. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.disc.2018.11.009

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/19104