Combinatorial $t$-Designs from Finite Abelian Groups and Their Applications to Elliptic Curve Codes

Exploring foci of: arXiv (Cornell University) Combinatorial $t$-Designs from Finite Abelian Groups and Their Applications to Elliptic Curve Codes May 2025 • H. Liu, Chunming Tang, Cuiling Fan, Rong Luo In this paper, we establish the conditions for some finite abelian groups and the family all the $k$-sets in each of them summing up to an element $x$ to form $t$-designs. We fully characterize the sufficient and necessary conditions for the incidence structures to form $1$-designs in finite abelian $p$-groups, generalizing existing results on vector spaces over finite fields. For finite abelian groups of exponent $pq$, we also propose sufficient and necessary conditions for the incidence structures to form a $1$-… Open Article Page

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