Title | Cyclic codes with lenght divisible by the field characteristic as invariant subspaces |
Publication Type | Journal Article |
Year of Publication | 2008 |
Authors | Radkova D, Bojilov A |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 98 |
Keywords | cyclic codes, invariant subspaces |
Abstract | 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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98-181-189.pdf | 724.75 KB |