Construction and nonexistence of strong external difference families

2017/01/20 by Jonathan Jedwab, Jedwab, Jonathan, Shuxing Li +1 · 2 citations
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.1701.05705

Abstract

Strong external difference families (SEDFs) were introduced by Paterson and Stinson as a more restrictive version of external difference families. SEDFs can be used to produce optimal strong algebraic manipulation detection codes. We characterize the parameters (v, m, k, λ) of a nontrivial SEDF that is near-complete (satisfying v=km+1). We construct the first known nontrivial example of a (v, m, k, λ) SEDF having m > 2. The parameters of this example are (243,11,22,20), giving a near-complete SEDF, and its group is ℤ₃⁵. We provide a comprehensive framework for the study of SEDFs using character theory and algebraic number theory, showing that the cases m=2 and m>2 are fundamentally different. We prove a range of nonexistence results, greatly narrowing the scope of possible parameters of SEDFs.

Cited by

• On circular external difference families
• Cyclotomic construction of λ-fold near-factorizations of cyclic groups

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