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We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a ...
Consider a subset $A$ of $\mathbb{F}_p^n$ and a decomposition of its indicator function as the sum of two bounded functions $1_A=f_1+f_2$. For every family of linear forms, we find the smallest degre...
In [1] we introduced a new sequence of linear positive operators Mn to approximate unbounded continuous functions of exponential growth on [0,\infty). As this sequence is saturated with O(n-1), to acc...
The system of weight equations for a binary (n, m)-code with respect to its ordered basis is introduced. It connects certain quantities (characteristics) related to the basis with the weights of non-z...
Some combinatorial problems concerning binary vector spaces are solved by applying the techniques developed in [1]. These illustrate that they are effective tools for such purposes.

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