arXiv subjects

Verónica Requena

Publications and source records attributed to Verónica Requena.

3 recordsLinked to original sources

arXiv2026

Construction of Generalized Weighing-Hadamard Matrices over Finite Fields

The existence, several properties, and constructions of Generalized Weighing-Hadamard (GWH) matrices over finite fields are addressed in this work. We study the subset of invertible GWH matrices and show that it forms a group under matrix multiplication. Besides that, we introduce a strong notion of equivalence between such matrices, defined via orthogonal transformations, and further prove that the corresponding quotient group by the subgroup of orthogonal matrices is abelian. Finally, we discuss some applications of these matrices in coding theory

cs.IT↗

arXiv2026

Binomial sequences over prime fields

The binary binomial sequences correspond to the diagonals of the Pascal's triangle modulo 2. They have interesting properties such as they form a basis of the linear space of all binary sequences with period a power of 2. Other properties of these sequences (period, linear complexity, construction rules or relations among different binomial sequences) have been deeply analysed in detail previously. In this work, we study the binomial $p$-ary sequences for a prime $p$, its intrinsic characteristic and formation rules. We also prove that the family of $p$-ary sequences with period a power of $p$ form a vector space over $\mathbb{F}_p$ and that the family of binomial $p$-ary sequences is a basis of this space.

math.NT↗

arXiv2023

Weighted Reed-Solomon convolutional codes

In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to the context of convolutional codes. For this reason we call them weighted Reed-Solomon (WRS) convolutional codes. We show that under some constraints on the defining parameters these codes are Maximum Distance Profile (MDP), which means that they have the maximal possible growth in their column distance profile. We study the size of the field needed to obtain WRS convolutional codes which are MDP and compare it with the existing general constructions of MDP convolutional codes in the literature, showing that in many cases WRS convolutional codes require significantly smaller fields.

cs.IT↗