Nonexistence of strong external difference families in abelian groups of order being product of at most three primes

Leung, Ka Hin; Li, Shuxing; Prabowo, Theo Fanuela

doi:10.1016/j.jcta.2020.105338

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…Some parameter sets can be ruled-out in certain classes of group using combinatorial or algebraic arguments. Non-existence results for SEDFs in abelian groups can be found in [1,4,8] and [10]. It is possible that SEDFs with some of these forbidden parameters may exist in non-abelian groups.…”

Section: Proposition 23 Necessary Conditions For the Existence Of Anmentioning

confidence: 99%

“…Does there exist a non-abelian SEDF whose parameters cannot be realised for an abelian SEDF? This is particularly relevant as the range of possible parameters for abelian SEDFs becomes increasingly constrained (in [8] it is conjectured that the known (243, 11, 22, 20)-SEDF is the only abelian SEDF with m > 2). Do there exist non-abelian SEDFs with m > 2?…”

Section: Concluding Remarks and Open Problemsmentioning

confidence: 99%

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Strong external difference families in abelian and non-abelian groups

2021

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Strong external difference families (SEDFs) have applications to cryptography and are rich combinatorial structures in their own right. We extend the definition of SEDF from abelian groups to all finite groups, and introduce the concept of equivalence. We prove new recursive constructions for SEDFs and generalized SEDFs (GSEDFs) in cyclic groups, and present the first family of non-abelian SEDFs. We prove there exist at least two non-equivalent (k2 + 1,2,k,1)-SEDFs for every k > 2, and begin the task of enumerating SEDFs, via a computational approach which yields complete results for all groups up to order 24.

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Section: Proposition 23 Necessary Conditions For the Existence Of Anmentioning

confidence: 99%

Section: Concluding Remarks and Open Problemsmentioning

confidence: 99%

Strong external difference families in abelian and non-abelian groups

2021

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Non-disjoint strong external difference families can have any number of sets

Huczynska,

2024

Arch. Math.

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Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application.

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Circular external difference families, graceful labellings and cyclotomy

Paterson,

Stinson

2024

Discrete Mathematics

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Nonexistence of strong external difference families in abelian groups of order being product of at most three primes

Cited by 3 publications

References 15 publications

Strong external difference families in abelian and non-abelian groups

Strong external difference families in abelian and non-abelian groups

Non-disjoint strong external difference families can have any number of sets

Circular external difference families, graceful labellings and cyclotomy

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