k-wise Set-Intersections and k-wise Hamming-Distances
Authors: Vince Grolmusz and Benny Sudakov
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 $a^1,a^2,\ldots,a^k$
of length $n$ have $k$-wise Hamming-distance $\ell$, if there are
exactly $\ell$ such coordinates, where not all of their coordinates
coincide (alternatively, exactly $n-\ell$ 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.
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