In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...

Z2Z4-additive codes have been defined as a subgroup of Z r 2 ×Z s 4 in [5] where Z2, Z4 are the rings of integers modulo 2 and 4 respectively and r and s positive integers. In this study, we define a new family of codes over the set Zr2[ξ̄] × Z s 4[ξ] where ξ is the root of a monic basic primitive polynomial in Z4[x]. We give the standard form of the generator and parity-check matrices of codes ...

A collection of functions addressing various modelling problems for nonlinear control systems has been developed in Mathematica environment. The mathematical apparatus behind the programs is based on the theory of non-commutative skew polynomial rings. The functions described in paper allow to find the state-space realization of the set of input-output equations, reduce the system equations, co...

For every ring R, we construct a ringed space NCSpec(R) and for every ring homomorphism R → S, a morphism of ringed spaces NCSpec(S) → NCSpec(R). We show that this gives a fully faithful contravariant functor from the category of rings to a category of ringed spaces. If R is a commutative ring, we show that NCSpec(R) can be viewed as a natural completion of Spec(R). We then explain how the spac...