Intersections of perfect binary codes
Olof Heden, F. I. Solov’eva, I. Yu. Mogilnykh · 2010
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) ≤ 2n-log(n+1)-2(n-1)/2, where the upper bound is attainable. We improve the upper bound and show that the intersection number 2n-log(n+1)-2(n-1)/2is ”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.