Polynomials over a ring that permute the matrices over that ring

On Skew Cyclic Codes over a Finite Ring

In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.

Uniformly Secondary Modules over Commutative Ring

In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.

Matroids over a ring

We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R = Z, and when R is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, respectively. More generally, whenever R is a Dedekind domain, we extend the...

A Theorem on Matrices over a Commutative Ring

One-stroke polynomials over a ring of modulo $2^w$

Permutation polynomials over a ring of modulo 2w are compatible with digital computers and digital signal processors, and so they are in particular expected to be useful for cryptography and pseudo random number generator. In general, the period of the polynomial should be long in such fields. In this paper, we derive the necessary and sufficient condition which specify one-stroke polynomials w...