On set systems with restricted intersections modulo p and p-ary t-designs

Set Systems with Restricted t-wise Intersections Modulo Prime Powers

We give a polynomial upper bound on the size of set systems with restricted t-wise intersections modulo prime powers. Let t ≥ 2. Let p be a prime and q = p be a prime power. Let L = {l1, l2, . . . , ls} be a subset of {0, 1, 2, . . . , q − 1}. If F is a family of subsets of an n element set X such that |F1 ∩ · · · ∩ Ft| (mod q) ∈ L for any collection of t distinct sets from F and |F | (mod q) /...

Set-Systems with Restricted Multiple Intersections

We give a generalization for the Deza-Frankl-Singhi Theorem in case of multiple intersections. More exactly, we prove, that if H is a set-system, which satisfies that for some k, the k-wise intersections occupy only ` residue-classes modulo a p prime, while the sizes of the members of H are not in these residue classes, then the size of H is at most (k − 1) ∑̀

Set Systems with Restricted Intersections modulo Prime Powers

We study set systems satisfying FrankllWilson-type conditions modulo prime powers. We prove that the size of such set systems is polynomially bounded, in contrast with V. Grolmusz's recent result that for non-prime-power moduli, no polynomial bound exists. More precisely we prove the following result. Theorem. Let p be a prime and q= p k. v For all i, j (1i< jm), there exists l (1ls) such that ...

Statistical Properties of Modulo-p Added p-Ary Sequences

Binary sequences are the most fundamental random numbers and have been extensively used in several applications such as spread-spectrum CDMA communications and cryptosystems. M-sequences, Kasami sequences, and Gold sequences, all of which can be generated by linear feedback shift registers (LFSRs), are well known as conventional binary sequences [1]. It is also well known that chaos phenomena c...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism