Abstract
Let \(\tilde \alpha = ({\alpha _{1,}}{\alpha _2}_{,...,}{\alpha _n})\) and \(\tilde \beta = ({\beta _{_1,}}{\beta _{_{2,}}}_{...,}{\beta _n})\) be tuples from B.n Remember that the number \(p(\tilde \alpha ,\tilde \beta ) = \sum _{i = 1}^n|{\alpha _i} - {\beta _i}|\) is called a distance (the Hamming distance) between vertices \(\tilde \alpha \) and \(\tilde \beta \)It is easy to check that the Hamming distance satisfies the metric axioms (see Problem 1.5.1.).
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© 1996 Springer Science+Business Media Dordrecht
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Gavrilov, G.P., Sapozhenko, A.A. (1996). Elements of Coding Theory. In: Problems and Exercises in Discrete Mathematics. Kluwer Texts in the Mathematical Sciences, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2770-9_5
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DOI: https://doi.org/10.1007/978-94-017-2770-9_5
Publisher Name: Springer, Dordrecht
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