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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

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Abstract

We suggest to prove the two following conjectures about the properties of some special functions.

First consider the following polynome in \(\lambda\in [0, (q-1)/q],\ q=2,3,\ldots \)

\(f^{q}_L (\lambda )=\sum\limits_{j_i :\ \sum_{i=1}^{q}j_i =L+1}\left( 1-\frac{\max\{ j_1 , \ldots ,j_q \}}{L+1}\right){L+1\choose j_1 ,\ldots ,j_{q}}\left(\frac{\lambda}{q-1}\right)^{L+1-j_q} (1-\lambda )^{j_q} .\)

It arise in the problem of obtaining the upper bound for the rate of multiple pa cking of q–ary Hamming space. The problem is to prove that this function is ∩–convex.

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© 2006 Springer-Verlag Berlin Heidelberg

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Blinovsky, V. (2006). Two Problems from Coding Theory. 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_72

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  • DOI: https://doi.org/10.1007/11889342_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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