Let R = GFiq^) be a Galois ring with identity e, characteristic p (p prime), and cardinality q, q = p, r e N. We say that a code C over the field Ρ = GF{q) is linearly representable over R if there exist a map σ : R —» P, d e N , and a linear code £ of length Ν over β (a submodule of the module R) such that C — a{JC) (σ acts on the words from K, coordinatewise). This construction was first used in [1] and [2] for the construction of a linear representation, over Z 4, of a dual Kerdock code. Later this result was published (in a weaker form) in [4], where a linear representation of the Preparata code was also constructed. At the same time, several non-linear cyclic codes over P, linearly representable over R, were described in [3]. Here we develop and sharpen the results of [3]. Linear codes can be described in terms of multilinear recurrences. An ideal / of a polynomial ring Vk = R[x], χ = (xi,. . . ,Xk), is said to be unitary if it contains unitary polynomials of the form Fi (JCI ) , · . · , Fk{xk). We say that / is a reversing ideal if xj 1 e,..., x'k k e 6 / for appropriate f j , . . . , ί* ε Ν. In what follows we assume that fι,..., tk are the smallest parameters with the indicated property. Let i 6 NQ and χ' = χ',' = •... · χ £. Then every polynomial A (x) e ? t has the form Α (χ) = £) jeflk aj-x'. Let R^" be the set of all fc-sequences over R, that is, of the functions u: NQ —> R, u = w(z t,..., zjt) = M(Z). We put v = A{x)-u, where υ = Λ<*>, u(z) = Σα?ί(ζ + /). Then /?<*> is a Vk-module. For a unitary ideal / of Vk, the submodule LR(I) = {u € /? ( t ' : / · u = 0} of this module is called the collection of fc-linear recurrent sequences over R. Let Π = {i\,..., iN} c NQ, and let LR{I,Π) be the set of vectors u[ITj = («(i'i,... ,u(iN)), where ueLR(I). Then Λ; = £ Κ (/,Π) is a linear code of length Ν over Λ, and every linear code over R can be represented in the indicated form for k^N. If / is a reversing ideal and Π = 0, t\ 1 χ . . . χ 0, tk 1, then K(I) = LK(I, Π) is a k-cyclic (multicyclic) code, that is, when s = 1,..., k, together with every word κ[Π] of K, the word («(i'i + e,), . . . , u{ ~iN + es)) also belongs to the code K, where e s is the ith row of the k χ k identity matrix, and the addition of the unit to the s\h coordinate of every vector i € Π is performed modulo t5. When k = 1 we obtain an ordinary cyclic code. The set of multicyclic codes over R coincides with the set of group codes K. < RG, where G is a finite Abelian group.