zbMATH — the first resource for mathematics

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 \(| C_{1} \cap C_{2}| = q\).

94B25 Combinatorial codes
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.