Let G be an abelian group. Suppose m 2 and |G| = v. Let D1, D2, · · · , Dm be mutually disjoint k-subsets of G. {D1, D2, · · · , Dm} is called a (v, m, k, λ)-strong external difference family (SEDF) in G if



 



Dj(t≠jDt-1=λ(G-1G) for each 1≤j≤m.



The study of SEDFs is motivated by the so called algebraic manipulation detection (AMD) codes, which can be regarded as a variation of classical authentication codes. Moreover, further cryptographic applications of AMD codes have been discovered later.



 



So far, only one nontrivial example exists for m ≥ 3. In this talk, I will present some recent non-existence results on abelian SEDF for m ≥ 3. Namely, we will show that if v is a product of three (not necessarily) primes, there is no SEDF unless G is p-elementary with prime p 3 × 1012 [1]. We also consider the case λ = pq where p, q are primes. It can be shown that for any fixed q, no SEDF exists if p is sufficiently large.

2021年12月16日
4pm - 5pm
地点
https://hkust.zoom.ust/j/9832399155 (Passcode: 322024)
讲者/表演者
Prof. Ka Hin LEUNG
National University of Singapore
主办单位
Department of Mathematics
联系方法
付款详情
对象
Alumni, Faculty and staff, PG students, UG students
语言
英语
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