Vasil’ev codes of length n = 2m and doubling of Steiner systems S(n, 4, 3) of a given rank

Vasil’ev codes of length n = 2m and doubling of Steiner systems S(n, 4, 3) of a given rank Extended binary perfect nonlinear Vasil’ev codes of length n = 2m and Steiner systems S(n, 4, 3) of rank n-m over F 2 are studied. The generalized concatenated construction of Vasil’ev codes induces a variant of the doubling construction for Steiner systems S(n, 4, 3) of an arbitrary rank r over F 2. We prove that any Steiner system S(n = 2m, 4, 3) of rank n-m can be obtained by this doubling construction and is formed by codewords of weight 4 of these Vasil’ev codes. The length 16 is studied in detail. Orders of the full automorphism groups of all 12 nonequivalent Vasil’ev codes of length 16 are found. There are exactly 15 nonisomorphic systems S(16, 4, 3) of rank 12 over F 2, and they can be obtained from codewords of weight 4 of the extended Vasil’ev codes. Orders of the automorphism groups of all these Steiner systems are found. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Vasil’ev codes of length n = 2m and doubling of Steiner systems S(n, 4, 3) of a given rank

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946006010029
Publisher site
See Article on Publisher Site

Abstract

Extended binary perfect nonlinear Vasil’ev codes of length n = 2m and Steiner systems S(n, 4, 3) of rank n-m over F 2 are studied. The generalized concatenated construction of Vasil’ev codes induces a variant of the doubling construction for Steiner systems S(n, 4, 3) of an arbitrary rank r over F 2. We prove that any Steiner system S(n = 2m, 4, 3) of rank n-m can be obtained by this doubling construction and is formed by codewords of weight 4 of these Vasil’ev codes. The length 16 is studied in detail. Orders of the full automorphism groups of all 12 nonequivalent Vasil’ev codes of length 16 are found. There are exactly 15 nonisomorphic systems S(16, 4, 3) of rank 12 over F 2, and they can be obtained from codewords of weight 4 of the extended Vasil’ev codes. Orders of the automorphism groups of all these Steiner systems are found.

Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 20, 2006

References

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