Abstract
The intersections of q-ary perfect codes are under study. We prove that there exist two q-ary perfect codes C 1 and C 2 of length N = qn + 1 such that |C 1 ⋂ C 2| = k · |P i |/p for each k ∈ {0,..., p · K − 2, p · K}, where q = p r, p is prime, r ≥ 1, \(n = \tfrac{{q^{m - 1} - 1}}{{q - 1}}\), m ≥ 2, |P i | = p nr(q−2)+n, and K = p n(2r−1)−r(m−1). We show also that there exist two q-ary perfect codes of length N which are intersected by p nr(q−3)+n codewords.
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Original Russian Text Copyright © 2008 Solov’eva F. I. and Los’ A. V.
The first author was partially supported by the Royal Swedish Academy of Sciences. The second author was supported by the Russian Science Support Foundation and the Integration Grant “Tree-Like Catalog of Mathematical Internet Resources” (No. 35) of the Siberian Division of the Russian Academy of Sciences. Both authors were partially supported by Novosibirsk State University.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 2, pp. 464–474, March–April, 2008.
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Solov’eva, F.I., Los’, A.V. Intersections of q-ary perfect codes. Sib Math J 49, 375–382 (2008). https://doi.org/10.1007/s11202-008-0036-6
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DOI: https://doi.org/10.1007/s11202-008-0036-6