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arXiv · 0902.2316

On weak isometries of Preparata codes

Ivan Yu. Mogilnykh
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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.

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Ivan Yu. Mogilnykh. 2009-02-20. On weak isometries of Preparata codes. https://arxiv.org/abs/0902.2316

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