The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian gro...

An [18,9,8] code Ce18 over GF(4) was constructed in [6] as an extended cyclic code, and Pless [9] describes the same code as an extended “Q-code”. This code is of particular interest since it is an extremal quaternary code: an [n, n/2, d] self-dual code with d = 2[n/6] + 2 ([6, p. 2951, [3, p. 2051). In the present note we give new coordinates for this code, enabling us to find a simple descrip...

Powerful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labelled with powers xn for binary encoded numbers n. It is shown that polynomial identity testing for powerful skew arithmetic circuits belongs to coRNC, which generalizes a corresponding result for (standard) skew circuits. Two applications of this result are presented...

A generalization of the cyclic Jacobi algorithm is proposed that works in an arbitrary compact Lie algebra. This allows, in particular, a unified treatment of Jacobi algorithms on different classes of matrices, such as, e.g., skew-symmetric or skew-Hermitian Hamiltonian matrices. Wildberger has established global, linear convergence of the algorithm for the classical Jacobi method on compact Li...

We design a non-commutative version of the Peterson-Gorenstein-Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In p...

In this paper, we study skew frame starters, which are strong starters that satisfy an additional “skew” property. We prove three new non-existence results for cyclic of certain types. also construct several small examples previously unknown by computer.

We investigate the notion of cyclicity for convolutional codes as it has been introduced in the papers [15, 18]. Codes of this type are described as submodules of F[z]n with some additional generalized cyclic structure but also as specific left ideals in a skew polynomial ring. Extending a result of [15], we show in a purely algebraic setting that these ideals are always principal. This leads t...