On binary linear codes and binary pseudo-random sequences

In this paper, we study the relation between the linear subspace of the pseudo-noise (PN)-sequences generated by a primitive polynomial and the simplex code. This family of sequences can be also seen as an Maximum Distance Separable (MDS) F2-linear code over Fr2. Furthermore, we see how to compute t...

Full description

Bibliographic Details
Authors: Cardell, Sara D. [UNESP], Climent, Joan-Josep, Requena, Verónica
Format: article
Status:Published version
Publication Date:2024
Country:Brasil
Institution:Universidade Estadual Paulista (UNESP)
Repository:Repositório Institucional da UNESP
Language:English
OAI Identifier:oai:repositorio.unesp.br:11449/296882
Online Access:http://dx.doi.org/10.1142/S0219498825500677
https://hdl.handle.net/11449/296882
Access Level:Open access
Keyword:generalized sequences
PN-sequences
Reed–Muller code
simplex code
Description
Summary:In this paper, we study the relation between the linear subspace of the pseudo-noise (PN)-sequences generated by a primitive polynomial and the simplex code. This family of sequences can be also seen as an Maximum Distance Separable (MDS) F2-linear code over Fr2. Furthermore, we see how to compute the family of generalized sequences produced by a primitive polynomial by means of a first-order Reed–Muller code.