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arXiv · 1509.03907

Binary Codes and Period-2 Orbits of Sequential Dynamical Systems

Colin Defant
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Abstract

Let $[K_n,f,π]$ be the (global) SDS map of a sequential dynamical system (SDS) defined over the complete graph $K_n$ using the update order $π\in S_n$ in which all vertex functions are equal to the same function $f\colon\mathbb F_2^n\to\mathbb F_2^n$. Let $η_n$ denote the maximum number of periodic orbits of period $2$ that an SDS map of the form $[K_n,f,π]$ can have. We show that $η_n$ is equal to the maximum number of codewords in a binary code of length $n-1$ with minimum distance at least $3$. This result is significant because it represents the first interpretation of this fascinating coding-theoretic sequence other than its original definition.

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Colin Defant. 2017-09-30. Binary Codes and Period-2 Orbits of Sequential Dynamical Systems. https://doi.org/10.23638/dmtcs-19-3-10

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