Abstract:
A subset (code) $V$ of a unit $n$-dimensional cube is characterized by a distance set $R(V)$ and parameters $n, M$, where $R(V)$ is the set of values taken by the Hamming distance between different code words; $n$ is the length; $M$ is the number of sets of the code. Let $M(n, R)$ denote the maximum of the parameter $M$ over all codes $V$ of length $n$ and with the distance set $R(V)\subset R$. Using information about the structure of the set $R$, we managed in a number of cases to improve the known upper bound for the metric functional $M(n, R)$.
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