Cyclic codes with lenght divisible by the field characteristic as invariant subspaces

ЗаглавиеCyclic codes with lenght divisible by the field characteristic as invariant subspaces
Вид публикацияJournal Article
Година на публикуване2008
АвториRadkova D, Bojilov A
СписаниеAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Том98
ключови думиcyclic codes, invariant subspaces
Резюме

In the theory of cyclic codes it is a common practice to require $(n,q)=1$, where $n$ is the word length and $F_q$ is the alphabet. However, much of the theory also goes through without this restriction on $n$ and $q$. We observe that the cyclic shift map is a linear operator in $F^n_q$. Our approach is to consider cyclic codes as invariant subspaces of $F^n_q$ with respect to this operator and thus obtain a description of cyclic codes in this more general setting.

2000 MSC

main 94B15, secondary 47A15

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