2018/05/03 by Huczynska, Sophie, Paterson, Maura B.
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1805.01330
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.