Let n be any fixed positive integer. Every circulant weighing matrix of weight n arises from what we call an irreducible orthogonal family of weight n. We show that the number of irreducible orthogonal families of weight n is finite and thus obtain a finite algorithm for classifying all circulant weighing matrices of weight n. We also show that, for every odd prime power q, there are at most fi...

In this paper we obtain [60,30,12], [64,32,12], [68,34,12], [72,36,12] doubly even self-dual codes as tailbitting convolutional codes with the smallest constraint length K=9. In this construction one information bit is modulo two add to the one of the encoder outputs and this row will replace the first row in the double circulant matrix. The pure double circulant construction with K=10 is also ...

Abstract: Let be a Gaussian Fibonacci skew-circulant matrix, and be a Gaussian Fibonacci left skew-circulant matrix, and both of the first rows are , where is the th Gaussian Fibonacci number, and is a nonnegative integer. In this paper, by constructing the transformation matrices, the explicit determinants of and are expressed. Moreover, we discuss the singularities of these matrices and the i...

Implicit time-step numerical integrators for ordinary and evolutionary partial di erential equations need, at each step, the solution of linear algebraic equations that are unsymmetric and often large and sparse. Recently, a block preconditioner based on circulant approximations for the linear systems arising in the boundary value methods (BVMs) was introduced by the author. Here, some circulan...

This paper presents method that offers the fast and accurate analysis of large-scale periodic array antennas by conjugate-gradient fast Fourier transform (CG-FFT) combined with an equivalent sub-array preconditioner. Method of moments (MoM) is used to discretize the electric field integral equation (EFIE) and form the impedance matrix equation. By properly dividing a large array into equivalent...

Recurrent Neural Networks (RNNs) are becoming increasingly important for time series-related applications which require efficient and real-time implementations. The recent pruning based work ESE (Han et al., 2017) suffers from degradation of performance/energy efficiency due to the irregular network structure after pruning. We propose block-circulant matrices for weight matrix representation in...

Recurrent Neural Networks (RNNs) are becoming increasingly important for time series-related applications which require efficient and real-time implementations. The recent pruning based work ESE (Han et al., 2017) suffers from degradation of performance/energy efficiency due to the irregular network structure after pruning. We propose block-circulant matrices for weight matrix representation in...

We propose geometrical methods for constructing square 01-matrices with the same number n of units in every row and column, and such that any two rows of the matrix have at most one unit in the same position. In terms of Design Theory, such a matrix is an incidence matrix of a symmetric configuration. Also, it gives rise to an n-regular bipartite graphs without 4-cycles, which can be used for c...

For a given nonnegative integer α, a matrix An of size n is called α-Toeplitz if its entries obey the rule An = [ar−αs] n−1 r,s=0. Analogously, a matrix An again of size n is called α-circulant if An = [ a(r−αs) modn ]n−1 r,s=0 . Such kind of matrices arises in wavelet analysis, subdivision algorithms and more generally when dealing with multigrid/multilevel methods for structured matrices and ...

Abstract. This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in wh...