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Diskretnyi Analiz i Issledovanie Operatsii, 2013, Volume 20, Issue 4, Pages 46–64
(Mi da739)
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This article is cited in 1 scientific paper (total in 1 paper)
Steiner quadruple systems of small ranks and extended perfect binary codes
D. I. Kovalevskayaa, F. I. Solov'evaba a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave.,
630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
Abstract:
Using the switching method, we give a classification of Steiner quadruple systems of order $N>8$ and rank $r_N$ (different by 2 from the rank of the Hamming code of length $N$) which are embedded into extended perfect binary codes of length $N$ and the same rank. Lower and upper bounds for the number of such different systems are provided. The lower bound and description of different Steiner quadruple systems of order $N$ and rank $r_N$ which are not embedded into extended perfect binary codes of length $N$ and the same rank are given. Tab. 4, bibliogr. 22.
Keywords:
Steiner quadruple system, extended perfect binary code, switching, $il$- and $ijkl$-components, rank.
Received: 11.10.2012 Revised: 06.06.2013
Citation:
D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small ranks and extended perfect binary codes”, Diskretn. Anal. Issled. Oper., 20:4 (2013), 46–64; J. Appl. Industr. Math., 7:4 (2013), 522–536
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https://www.mathnet.ru/eng/da739 https://www.mathnet.ru/eng/da/v20/i4/p46
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Abstract page: | 296 | Full-text PDF : | 83 | References: | 40 | First page: | 3 |
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