On Weak Isometries of Preparata Codes

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Two codes C1 and C2 are said to be weakly isometric if there exists a mapping J: C1 → C2 such that for all x, y in C1 the equality d(x, y) = d holds if and only if d(J(x), J(y)) = d, where d is the code distance of C1. 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.

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