Welington Santos
Mathematics · Coding Theory · Cryptography

Welington
Santos

Assistant Professor in the Department of Mathematics, Statistics, and Computer Science at the University of Wisconsin–Stout.

Explore my researchCurriculum vitae ↗
01 / About

Mathematics with purpose

My work connects coding theory, cryptography, and algebraic geometry. In research and in the classroom, I enjoy showing how abstract mathematical ideas can illuminate problems in communication, security, and computation.

Education

  1. August 2019

    Ph.D. in Mathematics

    Federal University of Paraná (UFPR) · Curitiba, Brazil

    Dissertation: Codes in the NRT-metric, Polynomial Invariant Theory, and Fractional decoding
    Advisor: Marcelo Muniz Silva Alves
    Co-advisor: Alexander Barg · University of Maryland

  2. July 2015

    M.Sc. in Mathematics

    Federal University of Paraná (UFPR) · Curitiba, Brazil

    Thesis: Códigos MDS na métrica de Niederreiter-Rosenbloom-Tsfasman e em métricas Poset
    Advisor: Marcelo Muniz Silva Alves

  3. February 2013

    B.Sc. in Mathematics

    State University of Ponta Grossa (UEPG) · Ponta Grossa, Brazil

Read my curriculum vitae
02 / Research

Areas of interest

1–3 of 6
01

Coding Theory

Algebraic methods for constructing and analyzing error-correcting codes.

A codeword passes through a noisy channel and is recovered by a decoderCODENOISEDECODERecovering information from errors
Error-correcting codes help recover information after transmission errors.
02

Algebraic geometric codes

Codes constructed from functions and points on algebraic curves.

Several marked evaluation points lie on a curve and map to a codewordCODEEvaluation points on a curve
Evaluating functions at points on a curve produces codewords.
03

Poset metric codes

Codes measured with distances defined by partial orders on coordinates.

A partial order of three coordinate positions and an ordered weight132ORDEREDWEIGHTDistance depends on coordinate order
A partial order changes how the weight of a codeword is measured.
04

Distributed Storage

Using codes to store data across multiple nodes and repair missing information.

A file is encoded into three storage nodes, with one node repaired from the othersFILENODE 1NODE 2NODE 3REPAIR
Encoded fragments spread across nodes can support recovery after failures.
05

Secure Distributed Computation

Dividing computations among servers while protecting private inputs.

Private input is split among three servers, whose results combine into an outputPRIVATESERVER 1SERVER 2SERVER 3RESULT
Servers contribute to a result without receiving the full private input.
06

Cryptography

Mathematical foundations of secure communication and computation.

A message and key enter encryption to produce ciphertextMESSAGEENCRYPTCIPHERKEYProtecting information with a key
Encryption transforms a message into ciphertext using a key.
Published work

Publications

  1. 2026
    Matrix Multiplication: Sharing Computation without Sharing Data

    C. Brock, M. Durisheti, C. Hinds, G. L. Matthews, and W. Santos · Mathematics Magazine, 99(3), 299–312

  2. 2025
    The Permutation Group of Reed-Solomon Codes Over Arbitrary Points

    E. Camps-Moreno, J. B. Lau, H. H. López, and W. Santos · IEEE International Symposium on Information Theory (ISIT), pp. 1–6

  3. 2025
    Fractional decoding and the Rosenbloom-Tsfasman metric

    W. Santos · Advances in Mathematics of Communications, 19(1), 304–318

  4. 2024
    Error correction from partial information via norm-trace codes

    E. Camps-Moreno, G. L. Matthews, and W. Santos · IEEE ISIT, pp. 2814–2819

  5. 2023
    Fractional decoding of r-Hermitian codes

    G. L. Matthews, A. W. Murphy, and W. Santos · Finite Fields and Their Applications, 92

  6. 2023
    HerA Scheme: Secure Distributed Matrix Multiplication via Hermitian Codes

    R. A. Machado, G. L. Matthews, and W. Santos · IEEE ISIT, pp. 1729–1734

  7. 2021
    Fractional decoding of codes from Hermitian curves

    G. L. Matthews, A. W. Murphy, and W. Santos · IEEE ISIT, pp. 515–520

  8. 2020
    Polynomial Invariant Theory and Shape Enumerator of Self-Dual Codes in the NRT-Metric

    W. Santos and M. M. Alves · IEEE Transactions on Information Theory, 66(7), 4061–4074

  9. 2019
    On Fractional Decoding of Reed-Solomon Codes

    W. Santos · IEEE ISIT, pp. 1552–1556

Presentations

Selected talks

  1. 2024

    Codes for secure distributed matrix multiplications

    Canadian Mathematical Society Winter Meeting · Vancouver, Canada · November

  2. 2024

    Unmasking deceitful servers: ensuring integrity in SDMM

    Joint Mathematics Meetings · San Francisco, California · January

  3. 2023

    HerA scheme: Secure distributed matrix multiplication via Hermitian codes

    IEEE International Symposium on Information Theory · Taipei, Taiwan · June

  4. 2023

    Gleason-Pierce-Ward Theorem for NRT metric codes

    Joint Mathematics Meetings · Boston, Massachusetts · January

  5. 2022

    NRT-metric codes—Duality theory

    AARG Seminar, Virginia Tech · Blacksburg, Virginia · October

  6. 2022

    Fractional decoding of Hermitian codes via interleaved Hermitian codes

    Virtual Joint Mathematics Meetings · April

  7. 2021

    Fractional decoding of codes from the Hermitian curve

    AMS Fall Central Sectional Meeting, Special Session on Coding, Storage, and Related Applications · October

  8. 2021

    Fractional decoding of codes from Hermitian curves

    IEEE International Symposium on Information Theory · Melbourne, Australia · July

  9. 2019

    On Fractional decoding of Reed-Solomon codes

    IEEE International Symposium on Information Theory · Paris, France · July

  10. 2018

    Invariant Theory and self-dual codes in the NRT-metric

    Latin American Week on Coding and Information · Campinas, Brazil · July

  11. 2017

    Invariant Theory and self-dual codes in the NRT-metric

    VII Journey of Information Theory · Campinas, Brazil · November

  12. 2016

    MDS codes in Niederreiter-Rosenbloom-Tsfasman metric

    II Brazilian Congress of Young Researchers in Pure and Applied Mathematics · Campinas, Brazil · December

  13. 2015

    A study of cyclic codes, BHC codes, and Reed-Solomon codes

    School of Advanced Science on Coding and Information Theory · Campinas, Brazil · January

  14. 2012

    Relations between matroids and families of linearly independent sets

    XXI Annual Meeting of Scientific Initiation · Maringá, Brazil · January

03 / Teaching

In the classroom

I teach across mathematics, computer science, and cybersecurity, connecting theory to problems students can explore and solve.

Teaching resources on my current site
MATH 150Calculus with Precalculus A
MATH 158Calculus III
CS 480Introduction to Computer Security
MATH150 · Class notesMATH158 · Class notes

Use the course password provided in class to access notes.

Teaching history

Courses taught previously

United States · 2023–2025

University of Wisconsin–Stout

MATH 150 · Calculus with Precalculus AFall 2024 (two sections)
MATH 151 · Calculus with Precalculus BFall 2023
MATH 153 · Calculus IFall 2023; Spring 2024 (two sections)
MATH 270 · Discrete MathematicsFall 2023; Spring 2025 (two sections); Fall 2025
MATH 275 · Linear AlgebraSpring 2025; Fall 2025
CS 480 · Introduction to Computer SecurityFall 2024; Spring 2025 (two sections); Fall 2025
MSCS 396 · Applied CryptographySpring 2024
United States · 2021–2023

Virginia Tech

Introduction to Linear Algebra
Specialized Topics in Algebra (graduate)
Cryptography
Brazil · 2021

Unicentro

Ordinary Differential Equations
Algebra
Differential Calculus
History of Mathematics
Probability and Statistics
Brazil · 2021

Federal Institute of Santa Catarina

Linear Algebra
Combinatorics
Algebra
Statistics
Applied Calculus
Analytic Geometry
Brazil · 2019–2020

Positivo University

Elementary Algebra (rings and groups)
Linear Algebra
Numerical Calculus
Introduction to Numerical Analysis
Euclidean and Non-Euclidean Geometries
Logic
04 / Community

Beyond the classroom

Research

Rethinking Number Theory

Project work on tensor products of generalized Reed–Solomon codes.

Workshop

ACTiV(T)

Helping organize a weeklong gathering in algebraic coding theory at Virginia Tech.

Outreach

Blacksburg Math Circle

Sharing coding theory and cryptography with young learners through hands-on mathematics.

More activities

05 / Contact

Get in touch

For questions about research, teaching, or collaboration:

santosw@uwstout.edu
University of Wisconsin–Stout

Department of Mathematics, Statistics, and Computer Science
225 Jarvis Hall, Science Wing
410 10th Ave E
Menomonie, WI 54751