Geodesic
Binary Codes and Period-2 Orbits of Sequential Dynamical Systems
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3

Voir la notice de l'article provenant de la source Episciences

Let $[K_n,f,\pi]$ be the (global) SDS map of a sequential dynamical system (SDS) defined over the complete graph $K_n$ using the update order $\pi\in S_n$ in which all vertex functions are equal to the same function $f\colon\mathbb F_2^n\to\mathbb F_2^n$. Let $\eta_n$ denote the maximum number of periodic orbits of period $2$ that an SDS map of the form $[K_n,f,\pi]$ can have. We show that $\eta_n$ 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. 
@article{DMTCS_2017_19_3_a6,
     author = {Defant, Colin},
     title = {Binary {Codes} and {Period-2} {Orbits} of {Sequential} {Dynamical} {Systems}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2017-2018},
     doi = {10.23638/DMTCS-19-3-10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-10/}
}
TY  - JOUR
AU  - Defant, Colin
TI  - Binary Codes and Period-2 Orbits of Sequential Dynamical Systems
JO  - Discrete mathematics & theoretical computer science
PY  - 2017-2018
VL  - 19
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-10/
DO  - 10.23638/DMTCS-19-3-10
LA  - en
ID  - DMTCS_2017_19_3_a6
ER  - 
%0 Journal Article
%A Defant, Colin
%T Binary Codes and Period-2 Orbits of Sequential Dynamical Systems
%J Discrete mathematics & theoretical computer science
%D 2017-2018
%V 19
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-10/
%R 10.23638/DMTCS-19-3-10
%G en
%F DMTCS_2017_19_3_a6
Defant, Colin. Binary Codes and Period-2 Orbits of Sequential Dynamical Systems. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3. doi: 10.23638/DMTCS-19-3-10

Cité par Sources :