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This article studies skew generalized quasi-cyclic codes (SGQC-codes) over finite fields for any length n. We derive generator polynomials and cardinality of SGQC codes. Moreover, we show that the dual of any length SGQC-code is also an SGQC-code. Our search results lead to the construction of fifteen new 2-generator SGQC codes over the finite field F 4 with minimum distances exceeding the minimum distances of the previously best known F 4 -linear codes with comparable parameters. [ABSTRACT FROM AUTHOR]

Abstract: The optimal control of transverse vibration of two Euler–Bernoulli beams coupled in parallel by discrete springs is considered. An index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving the point control forces. The minimization of the performance index over these forces is subject to the equation of motion governing the structural vibrations, the imposed initial condition as well as the boundary conditions. By use of the modal space technique, the optimal control of distributed parameter systems is simplified into the optimal control of a linear time-invariant lumped-parameter systems. A computationally attractive method based on Legendre wavelets in time domain for solving the optimal control of the lumped parameter systems for any finite interval is proposed. Legendre wavelet integral operational matrix and the properties of a Kronecker product are used to find the approximated optimal trajectory and optimal law of the linear systems with respect to a quadratic cost function by only solving a linear system of algebraic equations. This method provides a straightforward and convenient approach for digital computation. A numerical example is provided to demonstrate the applicability and effectiveness of the proposed method. [Copyright &y& Elsevier]

Cyclic codes of odd length over Z4 have been studied by many authors. But what is the form of cylic codes of even length? The structure of cyclic codes of length n=2e, for any positive integer e is considered. We show that any cyclic code is an ideal in the ring Rn=Z4[x]/〈xn−1〉. We show that the ring Rn is a local ring but not a principal ideal ring. Also, we find the set of generators for cyclic codes. Examples of cyclic codes of such length are given. [Copyright &y& Elsevier]

Abstract: Galerkin and wavelet methods for optimal boundary control of a couple of discretely connected parallel beams are proposed. First, the problem with boundary controls is converted into a problem with distributed controls. The problem is, then, reduced by a Galerkin-based approach into determining the optimal control of a linear time-invariant lumped parameter system, which will be solved by a wavelet-based method using Legendre wavelets. The integration-operational matrix and Kronecker product are utilized to significantly simplify the optimization problem into a system of linear equations. A numerical example is presented to demonstrate the applicability and the efficiency of the proposed method. [Copyright &y& Elsevier]