On k-wise set-intersections and k-wise 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 کاملK-wise Independence and -biased K-wise Indepedence
1 Deenitions Consider a distribution D on n bits x = x 1 x n. D is k-wise independent ii for all sets of k indices S = fi 1 x ik = a 1 a k ] = 1 2 k : The idea is that if we restrict our attention to any k positions in x, no matter how many times we sample from D, we cannot distinguish D from the uniform distribution over n bits. We can get a Fourier interpretation of k-wise independence by vie...
متن کاملAlmost k-wise independence versus k-wise independence
We say that a distribution over {0, 1} is ( , k)-wise independent if its restriction to every k coordinates results in a distribution that is -close to the uniform distribution. A natural question regarding ( , k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exists ( , k)-wise independent distribution whose statistical distance...
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: Journal of Combinatorial Theory, Series A
سال: 2002
ISSN: 0097-3165
DOI: 10.1006/jcta.2002.3264