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Family of two-dimensional correcting codes on a basis of perfect binary array

✍ Scribed by P. E. Baranov; M. I. Mazurkov; V. Ya. Chechelnytskyi; A. A. Yakovenko

Book ID: 111497722
Publisher: Allerton Press, Inc.
Year: 2009
Tongue: English
Weight: 68 KB
Volume: 52
Category: Article
ISSN: 0735-2727
DOI: 10.3103/s0735272709090088

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## Abstract The codewords at distance three from a particular codeword of a perfect binary one‐error‐correcting code (of length 2^m^−1) form a Steiner triple system. It is a longstanding open problem whether every Steiner triple system of order 2^m^−1 occurs in a perfect code. It turns out that thi