“St. Kl. OHRIDSKI” FACULTE ́ DE MATHÉMATIQUES ET INFORMATIQUE CYCLIC CODES AS INVARIANT SUBSPACES

In the coding theory the description of linear cyclic codes in terms of commutative algebra is well known. Since linear codes have the structure of linear subspaces of Fn, the description of linear cyclic codes in terms of linear algebra is natural. We observe that the cyclic shift map is a linear operator in Fn. Our approach is to consider cyclic codes as invariant subspaces of Fn with respect to this operator and thus obtain a description of cyclic codes