Related papers: Relative Generalized Minimum Distance Functions
Projective metrics on vector spaces over finite fields, introduced by Gabidulin and Simonis in 1997, generalize classical metrics in coding theory like the Hamming metric, rank metric, and combinatorial metrics. While these specific metrics…
Recently, Feng, Kuznetsov and Yang discovered a very general reduction formula for a sum of products of the generalized hypergeometric functions (J. Math. Anal. Appl. 443(2016), 116--122). The main goal of this note is to present a…
Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric…
We prove that the finite-difference based derivative-free descent (FD-DFD) methods have a capability to find the global minima for a class of multiple minima problems. Our main result shows that, for a class of multiple minima objectives…
Here we examine some connections between the notions of generalized arithmetic means, geodesics, Lagrange-Hamilton dynamics and Bregman divergences. In a previous paper we developed a predictive interpretation of generalized arithmetic…
This paper exploits Geometric (Clifford) Algebra (GA) theory in order to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from Geometric Calculus (GC),…
We present some recently obtained results on transverse-momentum dependent parton distribution functions (TMD PDFs), the latter being important ingredients for the description of semi-inclusive hadronic processes. Special attention is payed…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…
We consider linear codes over some fixed finite field extension over an arbitrary finite field. Gabidulin introduced rank metric codes, by endowing linear codes over the extension field with a rank weight over the base field and studied…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
We study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a finite field F_q. These codes appeared recently in a work by H. Lopez, C.…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its…
It is well-understood that different algorithms, training processes, and corpora produce different word embeddings. However, less is known about the relation between different embedding spaces, i.e. how far different sets of embeddings…
In this article we construct a new family of linear maximum rank distance (MRD) codes for all parameters. This family contains the only known family for general parameters, the Gabidulin codes, and contains codes inequivalent to the…
As we all know, many interesting and important codes are obtained by modifying or combining existing codes. In this paper, we focus on generalized Roth-Lempel (in short, GRL) codes and define a class of extended codes, i.e., the extended…
This paper explores the problem of generalized phase retrieval, which involves reconstructing a length-$n$ signal $\bm{x}$ from its $m$ phaseless samples $y_k = \left|\langle \bm{a}_k,\bm{x}\rangle\right|^2$, where $k = 1,2,...,m$, and…
We establish a normal approximation for the limiting distribution of partial sums of random Rademacher multiplicative functions over function fields, provided the number of irreducible factors of the polynomials is small enough. This…
Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of $q$-ary…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…