In this work we study codes characterized by the property that their parity check matrix is circulant, i.e., that rows are obtained as all the distinct cyclic shifts of the rst row. For these codes, we give simple expressions for their dimension and for a lower bound on their minimum distance. We also present an O(nd) algorithm to solve the problem of deciding whether codes satisfying given con...

The distance energy of a graph G is a recently developed energy-type invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast research for the pairs and families of non-cospectral graphs having equal distance energy, and most of these constructions were based on the join of graphs. A graph is called circulant if it is Cayley graph on the ...

In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and quadratic residue matrices. We provide conditions when can yield codes. of various lengths over F2 F2+uF2. Using extensions, neighbours sequences neighbours, many new particular, one code length 66 51 68.

In this paper, based upon the divide-and-conquer strategy, we propose a parallel algorithm for solving the circulant tridiagonal systems, which is simpler than the two previous algorithms proposed by Agui and Jimenez ( 1995) and Chung et al. ( 1995). Our algorithm can be easily generalized to solve the tridiagonal systems, the block-tridiagonal systems, and the circulant block-tridiagonal syste...

This paper presents a new type of circulant matrices. We call it the first and the last difference r-circulant matrix (FLDcircr matrix). We can verify that the linear operation, the matrix product and the inverse matrix of this type of matrices are still FLDcircr matrices. By constructing the basic FLDcircr matrix, we give the discriminance for FLDcircr matrices and the fast algorithm of the in...

In a distributed frequency-modulated continuous waveform (FMCW) radar system, the echo data collected are not in azimuth direction, so imaging effect of traditional range-Doppler (RD) algorithm is poor. Sparse Bayesian learning (SBL) an optimization based on theory that has been successfully applied to high-resolution because its strong robustness and high accuracy. However, SBL highly computat...

Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant and Toeplitz matrices in connection with recovery by `1-minization. In contrast to recent work in this direction we allow the use of an arbitrary subset of r...

Let F = (Kn,P) be a circulant homogeneous factorisation of index k, that means P is a partition of the arc set of the complete digraph Kn into k circulant factor digraphs such that there exists σ ∈ Sn permuting the factor circulants transitively amongst themselves. Suppose further such an element σ normalises the cyclic regular automorphism group of these circulant factor digraphs, we say F is ...