In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain rings. We study module structures and trace representations of QC codes, which lead to some lower bounds on the minimum Hamming distance of QC codes. Moreover, we investigate the structural properties of 1-generator QC codes. Under some conditions, we discuss the enumeration of 1-generator QC codes and describe how to o...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

We prove that when a pre-independence space satisfies some natural properties, then its cyclic flats form a bounded lattice under set inclusion. Additionally, we show that a bounded lattice is isomorphic to the lattice of cyclic flats of a pre-independence space. We also prove that the notion of cyclic width gives rise to dual-closed and minorclosed classes of B-matroids. Finally, we find a dif...

In this paper, we study skew cyclic and skew constacyclic codes over the ring R = Fq + uFq + vFq + uvFq where q = p^m; p is an odd prime, u^2 = u; v^2 = v; uv = vu. We show that Gray image of a skew cyclic code of length n is a skew quasi-cyclic code of length 4n over Fq of index 4. We also study the structural properties of skew cyclic and skew constacyclic codes over R. Further, generating po...

Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of ...

Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of ...

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...

We give the class of finite groups which arise as the permutation groups of cyclic codes over finite fields. Furthermore, we extend the results of Brand and Huffman et al. and we find the properties of the set of permutations by which two cyclic codes of length p can be equivalent. We also find the set of permutations by which two quasi-cyclic codes can be equivalent.

Although fatigue damage in bone induced by cyclic loading has been recognized as a problem of clinical significance, few fracture mechanics based studies have investigated how incipient cracks grow by fatigue in this material. In the present study, in vitro cyclic fatigue experiments were performed in order to quantify fatigue-crack growth behavior in human cortical bone. Crack-growth rates spa...