The $(n,m,k,\lambda)$-Strong External Difference Family with $m \geq 5$ Exists

Jiejing Wen; Minghui Yang; Keqin Feng

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arXiv · 1612.09495

The $(n,m,k,\lambda)$-Strong External Difference Family with $m \geq 5$ Exists

Jiejing Wen·Minghui Yang·Keqin Feng

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Abstract

The notion of strong external difference family (SEDF) in a finite abelian group $(G,+)$ is raised by M. B. Paterson and D. R. Stinson [5] in 2016 and motivated by its application in communication theory to construct $R$-optimal regular algebraic manipulation detection code. A series of $(n,m,k,\lambda)$-SEDF's have been constructed in [5, 4, 2, 1] with $m=2$. In this note we present an example of (243, 11, 22, 20)-SEDF in finite field $\mathbb{F}_q$ $(q=3^5=243).$ This is an answer for the following problem raised in [5] and continuously asked in [4, 2, 1]: if there exists an $(n,m,k,\lambda)$-SEDF for $m\geq 5$.

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Jiejing Wen, Minghui Yang, Keqin Feng. 2016-12-30. The $(n,m,k,\lambda)$-Strong External Difference Family with $m \geq 5$ Exists. https://arxiv.org/abs/1612.09495

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