Let $p$ be an odd prime, $q=p^e$, $e \geq 1$, and $\mathbb{F} = \mathbb{F}_q$ denote the finite field of $q$ elements. $f: \mathbb{F}^2\to \mathbb{F}$ $g: \mathbb{F}^3\to functions, let $P$ $L$ two copies 3-dimensional vector space $\mathbb{F}^3$. Consider a bipartite graph $\Gamma_\mathbb{F} (f, g)$ with vertex partitions edges defined as follows: for every $(p)=(p_1,p_2,p_3)\in P$ $[l]= [l_1,...

Permutations of the form \(F(x)=L_1(x^{-1})+L_2(x)\) with linear functions \(L_1,L_2\) are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence inverse function. In this paper, we show that F cannot be a permutation on binary fields if kernel \(L_1\) or \(L_2\) is large. A key step our proof an observation maximal size subspace V \(\mathbb {F}_{2^n}\) co...

The SPS-LASSO has recently been introduced as a solution to the problem of regularization parameter selection in the complex-valued LASSO problem. Still, the dependence on the grid size and the polynomial time of performing convex optimization technique in each iteration, in addition to the deficiencies in the low noise regime, confines its performance for Direction of Arrival (DOA) estimation....