Un schéma abélien correspond à un cas particulier de ce qui est habituellement nommé un anneau de Schur. Après un rappel des résultats dont on a besoin sur les codes additifs dans un schéma abélien, et leurs duaux, les schémas de translatés, les schémas métriques et les graphes distance-réguliers, les partitions cohérentes et les graphes complètement réguliers, nous donnons d’autres preuves de certains de ces résultats. De cette manière, nous obtenons une construction de schémas métriques abéliens et un algorithme pour calculer leurs matrices d’intersection.
An Abelian scheme corresponds to a special instance of what is usually named a Schur-ring. After the needed results have been quoted on additive codes in Abelian schemes and their duals, coset configurations, coset schemes, metric schemes and distance regular graphs, partition designs and completely regular codes, we give alternative proofs of some of those results. In this way we obtain a construction of metric Abelian schemes and an algorithm to compute their intersection matrices.
@article{AIF_1999__49_3_829_0,
author = {Camion, Paul and Courteau, Bernard and Montpetit, Andr\'e},
title = {Metric coset schemes revisited},
journal = {Annales de l'Institut Fourier},
volume = {49},
year = {1999},
pages = {829-859},
doi = {10.5802/aif.1695},
mrnumber = {2000g:05150},
zbl = {0917.05085},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1999__49_3_829_0}
}
Camion, Paul; Courteau, Bernard; Montpetit, André. Metric coset schemes revisited. Annales de l'Institut Fourier, Tome 49 (1999) pp. 829-859. doi : 10.5802/aif.1695. http://gdmltest.u-ga.fr/item/AIF_1999__49_3_829_0/
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