Weighted external difference families and R-optimal AMD codes

Sophie Huczynska; Maura Paterson

doi:10.1016/j.disc.2018.11.009

Weighted external difference families and R-optimal AMD codes

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	855-867
Journal	Discrete Mathematics
Volume	342
Issue number	3
Early online date	10 Dec 2018
DOIs	https://doi.org/10.1016/j.disc.2018.11.009
Publication status	Published - Mar 2019

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10.1016/j.disc.2018.11.009

WEDF_Huc_Pat_final
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
Accepted author manuscript, 325 KBLicence: CC BY-NC-ND

Difference families in coding and crypto: Difference families in coding and cryptography
Huczynska, S. (PI)
21/03/17 → 20/03/18
Project: Standard

Sophie Huczynska
- sh70st-andrews.acuk
- Pure Mathematics - Reader
- Centre for Interdisciplinary Research in Computational Algebra
Person: Academic

Cite this

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title = "Weighted external difference families and R-optimal AMD codes",

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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AB - 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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Weighted external difference families and R-optimal AMD codes

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Difference families in coding and crypto: Difference families in coding and cryptography

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Sophie Huczynska

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