On the symmetry group of the Mollard code

On the symmetry group of the Mollard code We study the symmetry group of a binary perfect Mollard code M(C,D) of length tm + t + m containing as its subcodes the codes C 1 and D 2 formed from perfect codes C and D of lengths t and m, respectively, by adding an appropriate number of zeros. For the Mollard codes, we generalize the result obtained in [1] for the symmetry group of Vasil’ev codes; namely, we describe the stabilizer $$Sta{b_{{D^2}}}$$ S t a b D 2 Sym(M(C,D)) of the subcode D 2 in the symmetry group of the code M(C,D) (with the trivial function). Thus we obtain a new lower bound on the order of the symmetry group of the Mollard code. A similar result is established for the automorphism group of Steiner triple systems obtained by the Mollard construction but not necessarily associated with perfect codes. To obtain this result, we essentially use the notions of “linearity” of coordinate positions (points) of a nonlinear perfect code and a nonprojective Steiner triple system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On the symmetry group of the Mollard code

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Publisher
Pleiades Publishing
Copyright
Copyright © 2016 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/S0032946016030042
Publisher site
See Article on Publisher Site

Abstract

We study the symmetry group of a binary perfect Mollard code M(C,D) of length tm + t + m containing as its subcodes the codes C 1 and D 2 formed from perfect codes C and D of lengths t and m, respectively, by adding an appropriate number of zeros. For the Mollard codes, we generalize the result obtained in [1] for the symmetry group of Vasil’ev codes; namely, we describe the stabilizer $$Sta{b_{{D^2}}}$$ S t a b D 2 Sym(M(C,D)) of the subcode D 2 in the symmetry group of the code M(C,D) (with the trivial function). Thus we obtain a new lower bound on the order of the symmetry group of the Mollard code. A similar result is established for the automorphism group of Steiner triple systems obtained by the Mollard construction but not necessarily associated with perfect codes. To obtain this result, we essentially use the notions of “linearity” of coordinate positions (points) of a nonlinear perfect code and a nonprojective Steiner triple system.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 19, 2016

References

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