The paper fully characterizes 1-designs from subset sums in finite abelian p-groups and exponent-pq groups, and links these designs to NMDS elliptic curve codes supporting 1-designs.
Cambridge University Press, Cambridge (1999)
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Combinatorial $t$-Designs from Finite Abelian Groups and Their Applications to Elliptic Curve Codes
The paper fully characterizes 1-designs from subset sums in finite abelian p-groups and exponent-pq groups, and links these designs to NMDS elliptic curve codes supporting 1-designs.