Codes over p-adic Numbers and Finite Rings Invariant under the Full Affine Group

Group Rings over the p-Adic Integers

On Codes that are Invariant under the Affine Group

Let k[V ] be the space of functions from a finite vector space into the algebraically closure of its field of scalars. This paper describes the lattice of subspaces of k[V ] which are invariant under the affine group AGL(V ). The description provides a simple method for finding the submodule generated by any set of functions given as polynomials in the standard coordinates.

Free Cyclic Codes as Invariant Submodules over Finite Chain Rings

By applying the theory of linear algebra, one can obtain some properties of these codes which generalize several well known results for free cyclic codes represented in [1, 4]. Mathematics Subject Classification: 94B05, 11T71, 47A15

Cyclic codes over finite rings

It is well known that cyclic linear codes of length n over a (finite) field F can be characterized in terms of the factors of the polynomial x"-1 in F[x]. This paper investigates cyclic linear codes over arbitrary (not necessarily commutative) finite tings and proves the above characterization to be true for a large class of such codes over these rings. (~) 1997 Elsevier Science B.V. All rights...

Linear Codes over Finite Rings

Linear codes over finite rings with identity have recently raised a great interest for their new role in algebraic coding theory and for their successful application in combined coding and modulation. Thus, in this paper we address the problems of constructing of new cyclic, BCH, alternant, Goppa and Srivastava codes over local finite commutative rings with identity. These constructions are ver...