Abstract
This paper continues the research of [1,2]. In [1] it was shown that a 1-perfect code is uniquely determined by its vertices at the middle levels of hypercube and in [2] the concerned formula was obtained. Now we prove that the vertices at the r-th level, r≤(n–1)/2, of such a code of length n uniquely determine all code vertices at the lower levels.
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References
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© 2006 Springer-Verlag Berlin Heidelberg
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Avgustinovich, S.V., Vasil’eva, A.Y. (2006). Testing Sets for 1-Perfect Code. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_59
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DOI: https://doi.org/10.1007/11889342_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46244-6
Online ISBN: 978-3-540-46245-3
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