In this paper we propose two metrics to be used in various fields of computational linguistics area. Our construction is based on the supposition that in most of the natural languages the most important information is carried by the first part of the unit. We introduce total rank distance and scaled total rank distance, we prove that they are metrics and investigate their max and expected value...

Scattered polynomials of a given index over finite fields are intriguing rare objects with many connections within mathematics. Of particular interest the exceptional ones, as defined in 2018 by first author and Zhou, for which partial classification results known. In this paper we propose unified algebraic description <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="...

In this paper, we properly extend the family of rank-metric codes recently found by Longobardi and Zanella (2021) Longobardi, Marino, Trombetti Zhou (2021). These are F q 2 t -linear dimension in space linearized polynomials over , where is any integer greater than 2, prove that they maximum rank distance codes. For ? 5 determine their equivalence classes these turn out to be inequivalent other...

This paper presents some computational properties of the Rank-Distance, a measure of similarity between partial rankings. We show how this distance generalizes the Spearman footrule distance, preserving its good computational complexity: the Rank-Distance between two partial rankings can be computed in linear time, and the rank aggregation problem can be solved in polynomial time. Further, we p...

Let Fq denote a finite field with q elements and let V = (Fq)m,n be the Fq-vector space of matrices over Fq of type (m,n). On V we define the so-called rank metric distance by d(A,B) = rank(A−B) for A,B ∈ V . Clearly, the distance d is a translation invariant metric on V . A subset C ⊆ V endowed with the metric d is called a rank metric code with minimum distance d(C) = min {d(A,B) | A 6= B ∈ V...

In 1991, Wei introduced generalized minimum Hamming weights for linear codes and showed their monotonicity and duality. Recently, several authors extended these results to the case of generalized minimum poset weights by using different methods. Here, we would like to prove the duality by using matroid theory. This gives yet another and very simple proof of it. In particular, our argument will ...

There are many algorithms for optimizing the search engine results, ranking takes place according to one or more parameters such as; Backward Links, Forward Links, Content, click through rate and etc. The quality and performance of these algorithms depend on the listed parameters. The ranking is one of the most important components of the search engine that represents the degree of the vitality...