On weak isometries of Preparata codes
Information Theory
2009-02-20 v3 math.IT
Abstract
Let C1 and C2 be codes with code distance d. Codes C1 and C2 are called weakly isometric, if there exists a mapping J:C1->C2, such that for any x,y from C1 the equality d(x,y)=d holds if and only if d(J(x),J(y))=d. Obviously two codes are weakly isometric if and only if the minimal distance graphs of these codes are isomorphic. In this paper we prove that Preparata codes of length n>=2^12 are weakly isometric if and only if these codes are equivalent. The analogous result is obtained for punctured Preparata codes of length not less than 2^10-1.
Cite
@article{arxiv.0902.2316,
title = {On weak isometries of Preparata codes},
author = {Ivan Yu. Mogilnykh},
journal= {arXiv preprint arXiv:0902.2316},
year = {2009}
}
Comments
Submitted to Problems of Information Transmission on 11th of January 2009