On weak isometries of Preparata codes

Details On weak isometries of Preparata codes On weak isometries of Preparata codes

2009-02-13

arxiv.org/abs/0902.2316v3

Computer Science

Information Theory

Submitted to Problems of Information Transmission on 11th of January 2009

Scientific paper

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.

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