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Weighted external difference families and R-optimal AMD codes

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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.
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Original languageEnglish
Pages (from-to)855-867
JournalDiscrete Mathematics
Volume342
Issue number3
Early online date10 Dec 2018
DOIs
Publication statusPublished - Mar 2019

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