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.
Problems of Information Transmission – Springer Journals
Published: Jul 18, 2009
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