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On intersection problem for perfect binary codes. (English) Zbl 1172.94640
Summary: The main result is that to any even integer $$q$$ in the interval $$0 \leq q \leq 2^{n+1-2\log(n +1)}$$, there are two perfect codes $$C_{1}$$ and $$C_{2}$$ of length $$n = 2^{m}-1$$, $$m \geq 4$$, such that $$| C_{1} \cap C_{2}| = q$$.

##### MSC:
 94B25 Combinatorial codes
##### Keywords:
Perfect binary codes
Full Text:
##### References:
 [1] Avgustinovich SV, Heden O, Solov’eva FI (2005). On intersections of perfect binary codes. to appear in the Proceedings of ALCOMA 05 [4] MacWilliams FJ, Sloane NJA (1977). The theory of error-correcting codes, Amsterdam North-Holland · Zbl 0369.94008 [6] Solov’eva FI (2004). On perfect codes and related topics, Com2Mac Lecture Note Series 13, Pohang 2004
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