Weeklong workshop fosters deep, rich mathematics collaboration in coding theory

Mathematicians present new developments at seminars, keep up with breakthroughs in the journals, and network at conferences — but when and where do they wade deep into the sticky problems with like-minded researchers?  For a small group of algebraic coding theorists, when was November 10-17, and where was Virginia Tech. 

Over the course of one week, mathematicians from five different institutions descended upon the Virginia Tech Blacksburg campus to share their work, brainstorm stumpers, and maximize expertise to make headway in the field of coding theory.

“This was a great opportunity to meet collaborators and to have the opportunity to discuss ideas in a friendly environment,” said Eduardo Camps Moreno, a graduate student from the Instituto Politécnico National. “It gave us the opportunity to discuss our results in a meaningful way, share ideas, and to propose several projects that will drive papers and new directions for research.”

Roberto Machado, a postdoc at Clemson University, describes “Since that was a full and intense week, we had time to make progress on bringing algebraic codes to secure distributed systems to reduce communication and computation costs in distributed computation. I also was able to participate in meetings for partnerships in IoT, smart farm, and cyber security projects, meeting researchers from Brazil.” 

The Algebraic Coding Theory at Virginia Tech — ACTiV(T) — workshop was hosted by the Virginia Tech Department of Mathematics and organized by Virginia Tech postdoctoral associates Giuseppe Cotardo and Wellington Santos along with faculty member  Gretchen Matthews.

ACTiV(T) builds on the ACCESS seminar and the Postgraduate International Coding Seminar (PICS) which are twice monthly online events. Since 2019, Matthews has run ACCESS to highlight world-class research in coding theory, cryptography, and related areas, in collaboration with colleagues at Clemson University and Florida Atlantic University. Cotardo is an organizer for PICS which provides platform for early-stage postdocs and PhD students to share their work and build connections as they enter the field. 

“ACTiV(T) at Virginia Tech has been a long-awaited meeting with researchers in coding theory,” said Felice Manganiello, associate professor in mathematics from Clemson University. 

 “The workshop fostered collaborations that will continue beyond the week.” Emily McMillon, RTG Lovett Instructor and postdoc at Rice University adds, “It was wonderful to interact with so many coding theorists of different career stages in a semi-formal environment. I hope similar events can become more commonplace in our field.”

Ariel Lui, seen below with McMillon, reflected on the experience, "ACTiV(T) week was a great opportunity for me to immerse myself in coding theory, learn about different research directions, meet coding theorists and mathematicians in person to ask questions. This increased communications with our research group will be helpful for my future research and study.”

The workshop cultivated and strengthened regional collaborations by drawing in new international partners.

“As a new postdoc with a network mainly centered in Europe, this event gave me the opportunity to become familiar with new topics in my research area and allowed me to start expanding my professional network in the U.S.,” said Cotardo.  

Julia Shapiro, a graduate student at Virginia Tech agreed, "Being a first year master’s student, I am lucky to have this type of event to expand my network in coding theory, make connections, listen to various topics in coding theory, and even present some of my research."

Workshop presentations from faculty researchers, postdocs, and graduate students were followed-up by working time for collaboration each day.

The one-hour presentations included:

• Benjamin Jany, University of Kentucky - A Critical Theorem for Rank Metric Codes
• Hiram H. López Valdez, Cleveland State University - Recent Results on Evaluation Codes
• Emily McMillon, Rice University - Cycles in Spatially-Coupled LDPC Codes
• Roberto Machado, Clemson University - Hybrid System for the Secure Multi-Party Computation Problem
• Felice Manganiello, Clemson University - An Attack on Generalized-error CVE ZK-ID Schemes
• Eduardo Camps Moreno, Instituto Politécnico National - Isometries of Classical Codes and Quantum Computation

The 20-minute talks by students and postdocs included:

• Giuseppe Cotardo, Virginia Tech - Parameters of Codes for the Binary Asymmetric Channel
• Ariel Liu, Virginia Tech - Spear and Shield: Coding to Thwart Adversarial Aggression
• William Mahaney, Virginia Tech - Lattice Based Approach to Decoding Multivariate Goppa Codes
• Aidan Murphy, Virginia Tech - Fractional Decoding of Norm-Trace-Lifted Codes
• Wellington Santos, Virginia Tech - Fractional Decoding of Algebraic Geometric Codes
• Julia Shapiro, Virginia Tech – Network Coding
• Freeman Slaughter, Clemson University - The CVE Zero-Knowledge Identification Scheme
• Luke Szramowski, Clemson University - Tensor Products in Polar Codes
• Stephen Timmel, Virginia Tech - Polar Coding in the Presence of Channel Memory 
• Stephen Timmel, Virginia Tech - Wiretap Channels and the Linear Extension Diameter of Polar Codes
• Daniel Valvo, Virginia Tech- Linear Exact Repair Schemes for Distributed Computation

ACTiV(T) was hosted by the Department of Mathematics and co-sponsored by the Commonwealth Cyber Initiative (CCI) Southwest Virginia, a regional node of the statewide Commonwealth Cyber Initiative, which serves as the primary access point for cybersecurity research, innovation, and workforce development. 

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