Diana Haidive Bueno

Pontificia Universidad Javeriana, Cali
2008 - Actualidad

Universidad del Valle
2007

Universidad Industrial de Santander
2003

I work on error-correcting coding theory (coding theory, for short), a sub-field of information theory.  Coding theory intersects mathematics and engineering, with applications to many areas of communication such as satellite and cellular phone transmission, data storage, etc. The main challenge in coding theory is to find codes having the largest number of words and error-correcting capabilities for optimum communication efficiency.  Constructing such optimal codes is still an open problem.  In practice, one or two parameters are fixed in order to find codes having the best possible value for the other(s) parameter(s).  

I develop techniques to design and construct codes whose parameters satisfy specific coding and error correcting needs.  Specifically, development of techniques for computing bounds for the minimum distance of algebraic codes as well as for designing and constructing codes with certain parameters.  All this from the study of the current bounds and the analysis of their construction, based on algebraic coding theory and techniques I developed.  I am also interested in the study of classic codes such as Reed-Solomon, Goppa, etc. with the aim of extending them to multiple variables.  

My work involves studying the properties of codes and their fitness for specific applications, including data compression, cryptography, error-correction and network coding.

Currently Funded Research
Group rings, partial actions and algebraic methods in error correcting codes and symbolic dynamics. Funded by the Spanish Ministry of Economics and Competitiveness under grant MTM2012-35240.

• R.A. Méndez-Romero, D.H. Bueno-Carreño, C. Díez-Fonnegra, and J.M. Redondo. "SIAM—Colombia MMC: A Challenge-Based Math Modeling Learning Strategy" Mathematics 9, no. 13 1565, 2021. https://doi.org/10.3390/math9131565
   
• Bernal, J.J., Bueno-Carreño, D.H. & Simón, J.J. “Constructions of Abelian Codes Multiplying Dimension of Cyclic Codes”. Math.Comput.Sci. 14, pp.415–421, 2020. https://doi.org/10.1007/s11786-019-00416-5
   
• D.H. Bueno-Carreño and J.A. Medina López. “Implementation of an algorithm to compute the strong apparent distance of bivariate codes” J. Phys.: Conf. Ser. 1160 012012, 2019.
   
• J.J. Bernal, D.H. Bueno-Carreño, and J.J. Simón. “Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound”. Advances in Mathematics of Communications, vol. 10, Issue 2, pp. 459 - 474, 2016.
   
• J.J. Bernal, D.H. Bueno-Carreño, and J.J. Simón. “Apparent distance and a Notion of BCH Multivariate Codes.” IEEE Trans. Inform. Theory, vol. 62, no. 2, pp. 655-668, 2016.
   
• D.H. Bueno-Carreño, J.J. Bernal and J.J. Simón. “A characterization of cyclic codes whose minimum distance equals their maximum BCH bound.” Extended abstract en ACA 2013 Proceedings, pp. 109 -113.
   
• D.H. Bueno-Carreño, J.J. Bernal and J.J. Simón. “Computing the Camion’s multivariate BCH bound.” Extended abstract en  ITW-Sevilla 2013 Proceedings, pp. 355-359.

Pontificia Universidad Javeriana seccional Cali
Grupo de investigación en Matemática y Estadística Aplicada-EMAP.
Departamento de Ciencias Naturales y Matemáticas.
Intereses de investigación: Teoría de la Información, particularmente la Teoría de códigos correctores de errores.

• Seleccionada como una de las 25 mujeres matemáticas colombianas que participaron del proyecto Mujeres matemáticas en Colombia. Un testimonio gráfico
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• Distinción de Profesor Destacado, Pontificia Universidad Javeriana seccional Cali. Mayo de 2018.
   
• Distinción de Profesor Destacado, Pontificia Universidad Javeriana seccional Cali. Mayo de 2022.

Asamblea directiva del Instituto GeoGebra Cali (IGCali).
Representante por la Pontificia Universidad Javeriana seccional Cali
2015 - Actualidad

Society for Industrial and Applied Mathematics CoSIAM
Vicepresidenta de la Junta directiva
2019 – Actualidad