On k-wise set-intersections and k-wise hamming-distances

摘要

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(1), a(2),..., a(k) of length n have k-wise Hamming-distance l, if there are exactly l such coordinates, where not all of their coordinates coincide (alternatively. exactly n - l of their coordinates are the same). We show a Delsarte-like upper bound: codes with few k-wise Hamming-distances must contain few code-words. (C) 2002 Elsevier Science (USA). [References: 15]