Geodesic
Arithmetic completely regular codes
Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3.

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

In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression. In order to better understand these "arithmetic completely regular codes", we focus on cartesian products of completely regular codes and products of their corresponding coset graphs in the additive case. Employing earlier results, we are then able to prove a theorem which nearly classifies these codes in the case where the graph admits a completely regular partition into such codes (e.g, the cosets of some additive completely regular code). Connections to the theory of distance-regular graphs are explored and several open questions are posed. 
@article{DMTCS_2016_17_3_a6,
     author = {Koolen, Jacobus and Sun Lee, Woo and Martin, William and Tanaka, Hajime},
     title = {Arithmetic completely regular codes},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2015-2016},
     doi = {10.46298/dmtcs.2150},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2150/}
}
TY  - JOUR
AU  - Koolen, Jacobus
AU  - Sun Lee, Woo
AU  - Martin, William
AU  - Tanaka, Hajime
TI  - Arithmetic completely regular codes
JO  - Discrete mathematics & theoretical computer science
PY  - 2015-2016
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2150/
DO  - 10.46298/dmtcs.2150
LA  - en
ID  - DMTCS_2016_17_3_a6
ER  - 
%0 Journal Article
%A Koolen, Jacobus
%A Sun Lee, Woo
%A Martin, William
%A Tanaka, Hajime
%T Arithmetic completely regular codes
%J Discrete mathematics & theoretical computer science
%D 2015-2016
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2150/
%R 10.46298/dmtcs.2150
%G en
%F DMTCS_2016_17_3_a6
Koolen, Jacobus; Sun Lee, Woo; Martin, William; Tanaka, Hajime. Arithmetic completely regular codes. Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3. doi : 10.46298/dmtcs.2150. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2150/

Cité par Sources :