Cyclotomic Construction of Strong External Difference Families in Finite Fields

2017/01/07 by Jiejing Wen, Minghui Yang, Wen, Jiejing +5 · 1 citation
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1701.01796

openalex publication_date 2017/01/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Strong external difference family (SEDF) and its generalizations GSEDF, BGSEDF in a finite abelian group G are combinatorial designs raised by Paterson and Stinson [7] in 2016 and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in G. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes.

Citations

• Accelerated Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein Polynomial
• New Existence and Nonexistence Results for Strong External Difference Families

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• Digraph-defined external difference families and new circular external difference families

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