Set systems with k-wise L-intersections and codes with restricted Hamming distances
نویسندگان
چکیده
منابع مشابه
On k-wise set-intersections and k-wise Hamming-distances
We prove a version of the Ray-Chaudhuri–Wilson and Frankl–Wilson theorems for k-wise intersections and also generalize a classical code-theoretic result of Delsarte for k-wise Hamming distances. A set of code-words a; a; . . . ; ak of length n have k-wise Hamming-distance ‘; if there are exactly ‘ such coordinates, where not all of their coordinates coincide (alternatively, exactly n ‘ of their...
متن کاملK-wise Set-intersections and K-wise Hamming-distances
We prove a version of the Ray-Chaudhuri{Wilson and Frankl-Wilson theorems for kwise intersections and also generalize a classical code-theoretic result of Delsarte for k-wise Hamming distances. A set of code-words a1; a2; : : : ; ak of length n have k-wise Hamming-distance `, if there are exactly ` such coordinates, where not all of their coordinates coincide (alternatively, exactly n ` of thei...
متن کاملExtremal set systems with restricted k-wise intersections
A large variety of problems and results in Extremal Set Theory deal with estimates on the size of a family of sets with some restrictions on the intersections of its members. Notable examples of such results, among others, are the celebrated theorems of Fischer, RayChaudhuri–Wilson and Frankl–Wilson on set systems with restricted pairwise intersections. These also can be considered as estimates...
متن کاملSet 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) /...
متن کاملSet-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) ∑̀
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2016
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2016.05.006