Abstract: In this talk, we propose a Tikhonov-like regularization for dynamical systems associated with non-expansive operators defined in closed and convex sets of a Hilbert space. We prove the well-posedness and the strong convergence of the proposed dynamical systems to a fixed point of the non-expansive operator. We apply the obtained result to the dynamical system associated with the problem of finding the zeros of the sum of a cocoercive operator with the subdifferential of a convex function. Posteriorly, we discuss an extension of Baillon-Haddad theorem, which particularly characterizes the cocoercive of the gradient of convex functions.
Rank-metric codes were introduced in 1978, but only in the last decade they have gained a lot of interest due to their application to network coding. These codes are linear subspaces of nxm matrices over a finite field Fq, but they can be also seen as subspaces of vectors of length n over an extension field Fqm. Codes that are optimal with respect to this metric are called Maximum Rank Distance (MRD) codes. The first and most studied construction of rank-metric codes was proposed in the seminal works of Delsarte (1978), Gabidulin (1985) and Roth (1991). These codes are known as generalized Gabidulin codes.