We define a class of automorphisms rational function fields finite characteristic and employ these to construct different types optimal linear rank-metric codes. The first construction is generalized Gabidulin codes over fields. Reducing fields, we obtain maximum rank distance (MRD) which are not equivalent twisted also Ferrers diagram settles further conjecture by Etzion Silberstein.

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.

The posetM(n) of all partitions of integers into distinct parts less than or equal to n has been widely studied during the last three decades. Among other properties, M(n) is self-dual, graded, rank-symmetric, rank-unimodal, strongly Sperner and, therefore, Peck [3, 4, 5]. This work presents a new description of M(n) through its isomorphic poset I(n) := ({0, 1} , ), that we have introduced in t...

We discuss the structure of negacyclic codes of odd length over the ring Fp[u, v]/〈u , v, uv − vu〉. We find the unique generating set, the rank and the minimum distance for these negacyclic codes.

Optimizing a stress model is a natural technique for drawing graphs: one seeks an embedding into Rd which best preserves the induced graph metric. Current approaches to solving the stress model for a graph with |V| nodes and |E| edges require the full all-pairs shortest paths (APSP) matrix, which takes O(|V|2 log |E|+ |V||E|) time and O(|V|2) space. We propose a novel algorithm based on a low-r...

We further the study of the duality theory of linear space-time codes over finite fields by showing that the only finite linear temporal correlated codes with a duality theory are the column distance codes and the rank codes. We introduce weight enumerators for both these codes and show that they have MacWilliams-type functional equations relating them to the weight enumerators of their duals. ...

Low-rank approximation with zeros aims to find a matrix of fixed rank and zero pattern that minimizes the Euclidean distance given data matrix. We study critical points this optimization problem using algebraic tools. In particular, we describe special linear, affine, determinantal relations satisfied by points. also investigate number how is related complexity nonnegative factorization problem.

A major challenge in Content-Based Image Retrieval (CBIR) is to bridge the semantic gap between low-level image contents and high-level semantic concepts. Although researchers have investigated a variety of retrieval techniques using different types of features and distance functions, no single best retrieval solution can fully tackle this challenge. In a real-world CBIR task, it is often highl...

We introduce the proximity rank join problem, where we are given a set of relations whose tuples are equipped with a score and a real-valued feature vector. Given a target feature vector, the goal is to return the K combinations of tuples with high scores that are as close as possible to the target and to each other, according to some notion of distance or dissimilarity. The setting closely res...

We formulate the problem of supervised hashing, or learning binary embeddings of data, as a learning to rank problem. Specifically, we optimize two common rankingbased evaluation metrics, Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). Observing that ranking with the discrete Hamming distance naturally results in ties, we propose to use tie-aware versions of ranking met...