On weak isometries of Preparata codes

On weak isometries of Preparata codes Two codes C 1 and C 2 are said to be weakly isometric if there exists a mapping J: C 1 → C 2 such that for all x, y in C 1 the equality d(x, y) = d holds if and only if d(J(x), J(y)) = d, where d is the code distance of C 1. We prove that Preparata codes of length n ≥ 212 are weakly isometric if and only if the codes are equivalent. A similar result is proved for punctured Preparata codes of length at least 210 − 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On weak isometries of Preparata codes

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946009020057
Publisher site
See Article on Publisher Site

Abstract

Two codes C 1 and C 2 are said to be weakly isometric if there exists a mapping J: C 1 → C 2 such that for all x, y in C 1 the equality d(x, y) = d holds if and only if d(J(x), J(y)) = d, where d is the code distance of C 1. We prove that Preparata codes of length n ≥ 212 are weakly isometric if and only if the codes are equivalent. A similar result is proved for punctured Preparata codes of length at least 210 − 1.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 18, 2009

References

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