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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
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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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