Abstract
Intersections of perfect binary codes are investigated. In 1998 Etzion and Vardy proved that the intersection number η(C, D), for any two distinct perfect codes C and D, is always in the range 0 ≤ η(C, D) ≤ 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-log(n+1)</sup> -2(n-1)/2, where the upper bound is attainable. We improve the upper bound and show that the intersection number 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-log(n+1)</sup> -2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n-1)/2</sup> is ”sporadic”. We also find a large class of intersection numbers for perfect binary codes of length 15 and for any admissible n > 15 a new set of intersection numbers for perfect codes of length n.
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