# Seminar of Algebra

### Trial set and Gröbner bases for binary codes

Speaker:
Mijail Borges (University of Oriente)
Email:
mijailbq@gmail.com
Location:
Departamento de Álgebra
Date:
Fri, 13 feb 2015 10:30
Mijail Borges is Professor of the Department of Mathematics, Faculty of Mathematics and Computer Sciences, University of Oriente, Santiago de Cuba. Research interests: Gröbner bases and applications, Coding theory, Cryptography.

We show the connections between trial sets and Gröbner bases for binary codes, which gives more characterizations of trial sets in the context of Gröbner bases and algorithmic ways for compute them. In this sense, minimal trial sets are characterized as trial sets associated with minimal Gröbner bases. We show also how for general linear codes the analysis is more complex and that similar problems can be extended and solved by means of a certain set of codewords we call leader codewords.

This talk is organised together with IMUS.