$m$-adic residue codes over $\mathbb{F}_q[v]/(v^s-v)$
Kuruz, Ferhat ; Temiz, Fatih ; Koroglu, Mehmet E.
arXiv, 1810.11826 / Harvested from arXiv
Text on arXiv
Due to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes. The $m$-adic residue codes are the generalization of the duadic codes. The aim of this paper is to study the structure of the $m$-adic residue codes over the quotient ring $\mathbb{F}_{q}[v]/(v^s-v).$ We determine the idempotent generators of the $m$-adic residue codes over $\mathbb{F}_{q}[v]/(v^s-v)$. We obtain some parameters of optimal $m$-adic residue codes over $\mathbb{F}_{q}[v]/(v^s-v),$ with respect to Griesmer bound for rings.
Publié le : 2018-10-28
Classification:  Computer Science - Information Theory 
@article{1810.11826,
     author = {Kuruz, Ferhat and Temiz, Fatih and Koroglu, Mehmet E.},
     title = {$m$-adic residue codes over $\mathbb{F}\_q[v]/(v^s-v)$},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1810.11826}
}

Kuruz, Ferhat; Temiz, Fatih; Koroglu, Mehmet E. $m$-adic residue codes over $\mathbb{F}_q[v]/(v^s-v)$. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1810.11826/