In this paper, skew cyclic and skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv=vu=0 are studied. We show that Gray image of a skew cyclic code of length n over R is a skew quasi-cyclic code of length 3n over F_q of index 3. Structural properties of skew cyclic and skew constacyclic over R are obtained. Further, gener...

In this paper we consider skew bisubmodular functions as recently introduced by the authors and Powell. We construct a convex extension of a skew bisubmodular function which we call Lovász extension in correspondence to the submodular case. We use this extension to show that skew bisubmodular functions given by an oracle can be minimised in polynomial time.

Recommended by Francois Goichot In this article, we study the relationship between left right zip property of R and skew polynomial extension over R, using the skew versions of Armendariz rings.

For certain subsets S and T of A = { · · · , (0, 2), (0, 1), (0, 0), (1, 0), (2, 0), · · · } and factor spaces C S [X, Y ], C +S,T [X, Y, Z,W ] and C − S,T [X, Y, Z,W ], bitableaux bases are constructed that are indexed by pairs of standard tableaux and sequences in the collections ΥψS and ΥψT . These bases give combinatorial interpretations to the appropriate Hilbert series of these spaces as ...

Two canonical forms for skew-symmetric matrix polynomials over arbitrary fields are characterized — the Smith form, and its skew-symmetric variant obtained via unimodular congruences. Applications include the analysis of the eigenvalue and elementary divisor structure of products of two skew-symmetric matrices, the derivation of a Smith-McMillan-like canonical form for skew-symmetric rational m...

We show that error and erasure decoding of `-Interleaved Gabidulin codes, as well as list-` decoding of Mahdavifar–Vardy codes can be solved by row reducing skew polynomial matrices. Inspired by row reduction of F[x] matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into certain normal forms. We apply this to solve generalised shift registe...

In this paper, we study the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras.

When R is a local ring with a nilpotent maximal ideal, the Ore extension R[x;σ, δ] will or will not be 2-primal depending on the δ-stability of the maximal ideal of R. In the case where R[x;σ, δ] is 2-primal, it will satisfy an even stronger condition; in the case where R[x;σ, δ] is not 2-primal, it will fail to satisfy an even weaker condition. 1. Background and motivation In [13, Proposition ...