5 research outputs found
Binary Codes and Period-2 Orbits of Sequential Dynamical Systems
Let be the (global) SDS map of a sequential dynamical system
(SDS) defined over the complete graph using the update order
in which all vertex functions are equal to the same function . Let denote the maximum number of periodic
orbits of period that an SDS map of the form can have. We
show that is equal to the maximum number of codewords in a binary code
of length with minimum distance at least . This result is significant
because it represents the first interpretation of this fascinating
coding-theoretic sequence other than its original definition.Comment: 12 pages, 2 figure