Henry Chimal-Dzul
Department of Mathematics
University of Notre Dame
255 Hurley Bldg
Notre Dame, IN 46556-4618
E-Mails
Research
Research Interests
My research interests include theoretical and applied aspects of coding theory and cryptography as well as topics in algebra, ring theory, module theory and computational algebra.
My current research focuses on investigating algebraic properties and parameters of quas-cyclic codes. Special emphasis is devoted to the subfamilies of quasi-cyclic low density parity check codes (QC-LDPC codes) and quasi-cyclic moderate density parity check codes (QC-MDPC codes), where my interest is to discover novel algebraic constructions, decoding algorithms, lower minimum distance bounds and their impact in Code-based cryptography. QC-LDPC codes represent the current state of the art in error-correction, while QC-MDPC codes lie in the heart of the code-based cryptosystems BIKE and HQC, which are finalists in the NIST Post-Quantum Cryptography Standardization. In addition to these topics, I am also interested on Symbolic Computation, I am a member of the group that is developing a Coding Theory package for Macaulay2. I am also developing MAGMA code for classical topics in Coding Theory.
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Publications (Most recent first)
12. H. Chima-Dzul, N. Gassner, R. Schnyder, J. Rosenthal, Efficient description of some classes of codes using group algebras. IFAC Papers (2022).
11. H. Chima-Dzul, J. Lieb, J. Rosenthal, Generator Matrices for Quasi-cyclic codes over Extension Fields Obtained from Gröbner Basis. IFAC Papers (2022).
10. H. Chimal-Dzul, Commutative polynomial rings which are principal ideal rings, Algebra and Related Topics with Applications. (2022)
9. H. Chimal-Dzul, S. Lopez-Permouth, S. Szabo, Abelian right McCoy rings and related notions. São Paulo J. Math. Sci. (2022).
8. T. Ball, et al., Coding Theory Package for Macaulay2, Journal of Software for Algebra and Geometry 11 (2021).
7. H. Chimal-Dzul, S. Szabo, Classification of nonsemicommutative rings, Acta Mathematica Hungarica (2021).
6. H. Chimal-Dzul, S. Lopez-Permouth, S. Szabo. Characterizations of certain Morita context rings, (2021) Communications in Algebra.
5. H. Chimal-Dzul, S. Szabo, Minimal reflexive nonsemicommutative rings, (2021) Journal of Algebra and its Applications.
4. H. Chimal-Dzul, C.A. Lopez-Andade, When is R[x] a principal ideal ring?, Rev. Int., 35 (2018), No. 2, 143-148.
3. R. Fernandez-Alonso, S. Gavito, H. Chimal-Dzul, A class of rings for which the lattice of preradicals is not a set, IEJA, 9 (2011), 38-60.
2. H. Chimal-Dzul, J. Diaz-Vargas, An Optimal Linear Code over F11, Lecturas Matemáticas (SMC), 30 (2009), No. 2, 2009, 63-72.
H. Chimal-Dzul, J. Diaz-Vargas, La forma normal algebraica de una función boolena, Miscelánea Matemática (SMM), 48 (2009), 47-57.
Preprints
H. Chimal-Dzul and J. Lieb, Convolutional codes.
H. Chimal-Dzul and A. Gomez-Fonseca, Shortest quasi-cyclic low density parity check codes based on protographs.