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Some nonexistence results for (v,m,k,pq)-strong external difference families
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2021-12-23 , DOI: 10.1016/j.jcta.2021.105575
Ka Hin Leung , Theo Fanuela Prabowo

In this paper, we derive some restrictions and nonexistence results for (v,m,k,pq)-strong external difference families (SEDFs), where p and q are primes. We first show that there is no abelian (v,m,k,p2)-SEDF with m>2. If p>q, we show that if q+1 is a power of two; or q+1=2r or 4r for some prime r>3, then there is no abelian (v,m,k,pq)-SEDF with m>2 for all sufficiently large primes p. Furthermore, we completely rule out the existence of abelian (v,m,k,pq)-SEDF with m>2 in case q=2,3,5,7,13,19,31.



中文翻译:

(v,m,k,pq)-强外部差异族的一些不存在结果

在本文中,我们推导出了一些限制和不存在的结果 (v,,,pq)- 强外部差分族 (SEDF),其中pq是素数。我们首先证明不存在阿贝尔(v,,,p2)-SEDF 与 >2. 如果p>q,我们证明如果 q+1是二的幂;或者q+1=2r或 4 r为一些素数r>3,那么没有阿贝尔 (v,,,pq)-SEDF 与 >2对于所有足够大的素数p。此外,我们完全排除了阿贝尔的存在(v,,,pq)-SEDF 与 >2 以防万一 q=2,3,5,7,13,19,31.

更新日期:2021-12-23
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