Binary codes and period-2 orbits of sequential dynamical systems

被引：0

作者：

Defant, Colin ^{[1
,2
]}

机构：

[1] Princeton University, United States

[2] University of Florida, United States

来源：

Discrete Mathematics and Theoretical Computer Science | 2017年 / 19卷 / 03期

关键词：

D O I：

10.23638/DMTCS-19-3-10

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学科分类号：

摘要：

Let [Kn, f, π] be the (global) SDS map of a sequential dynamical system (SDS) defined over the complete graph Kn using the update order π ∈ Sn in which all vertex functions are equal to the same function f : Fn2 → Fn2 . Let ηn denote the maximum number of periodic orbits of period 2 that an SDS map of the form [Kn, f, π] can have. We show that ηn 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. © 2017 by the author(s).

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