In this paper we settle the question of whether a finite-dimensional vector space V over F_p, with p an odd prime, and the family of all the k-sets of elements of V summing up to a given element x, form a 1-(v, k, λ_1) or a 2-(v, k, λ_2) block design, and, in either case, we find a closed form for λ_i and characterize the automorphism group. The question is discussed also in the case where the elements of the k-sets are required to be all nonzero, as the two cases happen to be intrinsically inseparable. The "twin case" p = 2, which has strict connections with coding theory, was completely discussed in a recent paper by G. Falcone and the present author.

Pavone, M. (2023). Subset sums and block designs in a finite vector space. DESIGNS, CODES AND CRYPTOGRAPHY, 91(7), 2585-2603 [10.1007/s10623-023-01213-9].

Subset sums and block designs in a finite vector space

Pavone, Marco
2023-07-01

Abstract

In this paper we settle the question of whether a finite-dimensional vector space V over F_p, with p an odd prime, and the family of all the k-sets of elements of V summing up to a given element x, form a 1-(v, k, λ_1) or a 2-(v, k, λ_2) block design, and, in either case, we find a closed form for λ_i and characterize the automorphism group. The question is discussed also in the case where the elements of the k-sets are required to be all nonzero, as the two cases happen to be intrinsically inseparable. The "twin case" p = 2, which has strict connections with coding theory, was completely discussed in a recent paper by G. Falcone and the present author.
lug-2023
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
Pavone, M. (2023). Subset sums and block designs in a finite vector space. DESIGNS, CODES AND CRYPTOGRAPHY, 91(7), 2585-2603 [10.1007/s10623-023-01213-9].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/609733
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