Abstract. Given any finite field Fq, an (N, K) quasi cyclic code is defined as a K dimensional linear subspace of Fq u which is invariant under T" for some integer n, 0 < n =< N, and where T is the cyclic shift operator. Quasi cyclic codes are shown to be isomorphic to the Fq[2]-submodules of Fq u where the product #(2).v is naturally defined as #o v + #1vT" + ... + #,,vT m" if #(2) = #o + #1 ' ;~ + "" + #,, 2m. In the case where (N/n, q)= 1, all quasi cyclic codes are shown to be decomposable into the direct sum of a fixed number of indecomposable components called irreducible cyclic Fq[2]-submodules providing for the complete characterisation and enumeration of some subclasses of quasi cyclic codes including the cyclic codes, the quasi cyclic codes with a cyclic basis, the maximal and the irreducible ones. Finally a general procedure is presented which allows for the determination and characterisation of the dual of any quasi cyclic code.
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