An upper bound on the size of a code with $s$ distances

March 11, 2025 · The Ethereal · 🏛 arXiv.org

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Authors Ivan Landjev, Konstantin Vorobev arXiv ID 2503.08948 Category math.CO: Combinatorics Cross-listed cs.IT Citations 0 Venue arXiv.org Last Checked 3 months ago
Abstract
Let $C$ be a binary code of length $n$ with distances $0<d_1<\cdots<d_s\le n$. In this note we prove a general upper bound on the size of $C$ without any restriction on the distances $d_i$. The bound is asymptotically optimal.
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