Let G be a finite abelian group. We will consider a skew product extension of a product of two Cantor minimal Z-systems associated with a G-valued cocycle. When G is non-cyclic and the cocycle is non-degenerate, it will be shown that the skew product system has torsion in its coinvariants.

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.

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 Gray code is said to be cyclic if the last element and the first element in the sequence also differ by some pre-specified constant amount. The Gray code above demonstrates the cyclic property. It is well known that a cyclic Gray code of binary string corresponds to a Hamilton cycle in the n-dimensional hypercube. Figure 1 shows the 3-dimensional hypercube Q3 with the Hamilton cycle correspon...

A (cyclic) n-bit Gray code is a (cyclic) ordering of all 2 binary strings of length n such that consecutive strings differ in a single bit. Equivalently, an nbit Gray code can be viewed as a Hamiltonian path of the n-dimensional hypercube Qn, and a cyclic Gray code as a Hamiltonian cycle of Qn. In this paper we study Hamiltonian paths and cycles of Qn avoiding a given set of faulty edges that f...

A (cyclic) n-bit Gray code is a (cyclic) ordering of all 2 binary strings of length n such that consecutive strings differ in a single bit. Equivalently, an n-bit Gray code can be viewed as a Hamiltonian path of the n-dimensional hypercube Qn, and a cyclic Gray code as a Hamiltonian cycle of Qn. In this paper we study (cyclic) Gray codes avoiding a given set of faulty edges that form a matching...

It is shown that the extended quadratic residue code of length 20 over GF(7) is a unique self-dual [20, 10, 9] code C such that the lattice obtained from C by Construction A is isomorphic to the 20-dimensional unimodular lattice D 20, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.

In this paper we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalization of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without ...

Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of x − λ, where λ is a unit element, are exhibited. When λ = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined tog...