<p>The modern digital world comprises of transmitting media files like image, audio, and video which leads to usage large memory storage, high data transmission rate, a lot sensory devices. Compressive sensing (CS) is sampling theory that compresses the signal at time acquiring it. samples efficiently below Nyquist rate minimize storage recoveries back significantly minimizing few sensors...

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 main goal of this article is to establish several new \({\mathbb {A}}\)-numerical radius equalities for \(n\times n\) circulant, skew imaginary tridiagonal, and anti-tridiagonal operator matrices, where {A}}\) the diagonal matrix whose entries are positive bounded A. Some special cases our results lead earlier works in literature, which shows that more general. Further, some pinching type i...

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 we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

In this paper, we consider a g-circulant matrixA 1(T), whose the first row entries are generalized Tribonacci numbers T(a)i. We give an explicit formula of spectral norm matrix. When g = 1, also present upper and lower bounds for spread 1-circulant matrix A1(T).

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 ...