Note: on k-wise set-intersections and k-wise Hamming-distances

Authors:
Vince Grolmusz;Benny Sudakov
Affiliations:
Department of Computer Science, Eö/tvö/s University, Budapest, Pá/zmá/ny P. stny. 1/C, H-1117 Budapest, Hungary;Department of Mathematics, Princeton University, Princeton, New Jersy 08540/ and Institute for Advanced Study, Princeton, New Jersy
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

Citing 4
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Abstract

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 a1, a2,...,ak 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.