Quasi-cyclic (QC) codes form an important generalization of cyclic codes. It is well know that QC codes of length sl with index s over the finite field F are F[y]-submodules of the ring F[x, y]/< x − 1, y − 1 >. The aim of the present paper, is to study QC codes of length sl with index s over the finite field F and find generator polynomials and generator matrix for these codes. To achieve this...

In this note we show that a Noetherian module has a dual module if and only if it satisfies AB5*. A connection between completeness and AB5* is also established. In this note we relate completeness, quasi-completeness, the A B5* condition, and duality. The main result is that a Noetherian R-module has a dual module if and only if it satisfies A B5*. Throughout this note R will denote a commutat...

Time series analysis is the statistical approach used to analyze a of data. most popular method for forecasting, which widely in several and economic applications. The wavelet transform powerful mathematical technique that converts an analyzed signal into time-frequency representation. provides information both time domain frequency domain. aims this study are propose function by derivation quo...

The concept of a 2-Absorbing submodule is considered as an essential feature in the field module theory and has many generalizations. This articale discusses Extend Nearly Pseudo Quasi-2-Absorbing submodules their relationship to submodule, Nearly-2-Absorbing Pseudo-2-Absorbing rest other concepts previously studied. between them been studied, explaining that opposite not true under certain con...