On mobile sets in the binary hypercube

Details On mobile sets in the binary hypercube On mobile sets in the binary hypercube

2008-02-01

arxiv.org/abs/0802.0003v1

Diskretn. Anal. Issled. Oper. 15(3) 2008, 11-21 (in Russian)

Mathematics

Combinatorics

9p., in Russian (English version will be finished later)

Scientific paper

If two distance-3 codes have the same neighborhood, then each of them is
called a mobile set. In the (4k+3)-dimensional binary hypercube, there exists a
mobile set of cardinality 2*6^k that cannot be split into mobile sets of
smaller cardinalities or represented as a natural extension of a mobile set in
a hypercube of smaller dimension. Keywords: mobile set; 1-perfect code.

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