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

✍ Scribed by Vince Grolmusz; Benny Sudakov

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 135 KB
• Volume: 99
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.2002.3264

✦ Synopsis

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 '; if there are exactly ' such coordinates, where not all of their coordinates coincide (alternatively, exactly n À ' of their coordinates are the same). We show a Delsarte-like upper bound: codes with few k-wise Hammingdistances must contain few code-words. # 2002 Elsevier Science (USA)