In this paper we generalize coding theory of cyclic codes over finite fields to skew polynomial rings over finite rings. Codes that are principal ideals in quotient rings of skew polynomial rings by two sided ideals are studied. Next we consider skew codes of endomorphism type and derivation type. And we give some examples.

Skew cyclic codes play the same role as cyclic codes in the theory of errorcorrecting codes for the rank metric. In this paper, we give descriptions of these codes by idempotent generators, root spaces and cyclotomic spaces. We prove that the lattice of skew cyclic codes is anti-isomorphic to the lattice of root spaces and extend the rank-BCH bound on their minimum rank distance to rank-metric ...

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle x^{n}-1\rangle and construct their generators and minimal generating sets. Also, an algorithm has been provided to encode and decode these skew cyclic codes.

In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided quadrilateral plates but as a special case, the numerical results f...

Let GF (q) denote the Galois field of q elements, and let V (n, q) denote the vector space of all ordered n-tuples over GF (q). The number of nonzero positions in a vector x ∈ V (n, q) is called the Hamming weight wt(x) of x. The Hamming distance d(x,y) between two vectors x,y ∈ V (n, q) is defined by d(x,y) = wt(x − y). A linear code C of length n and dimension k over GF (q) is a k-dimensional...

In this work the definition of codes as modules over skew polynomial rings of automorphism type is generalized to skew polynomial rings, whose multiplication is defined using an automorphism and a derivation. This produces a more general class of codes which, in some cases, produce better distance bounds than module skew codes constructed only with an automorphism. Extending the approach of Gab...

Let A be a ring with identity, id="M2"> σ endomorphism of id="M3"> that maps the identity to itself, id="M4"> δ id="M5"> -derivation id="M6"> , and consider skew-polynomial id="M7"> X ; , . When id="M8"> is ...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

A (v, k, λ) optical orthogonal code C is a family of (0, 1) sequences of length v and weight k satisfying the following correlation properties: (1) ∑ 0≤t≤v−1xtxt+i ≤ λ for any x = (x0, x1, . . . , xv−1) ∈ C and any integer i ̸≡ 0 (mod v); (2) ∑ 0≤t≤v−1xtyt+i ≤ λ for any x = (x0, x1, . . . , xv−1) ∈ C, y = (y0, y1, . . . , yv−1) ∈ C with x ̸= y, and any integer i, where the subscripts are taken mo...