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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > BIMSA-YMSC Tsinghua Number Theory Seminar Duals of linearized Reed-Solomon codes
Duals of linearized Reed-Solomon codes
Organizers
Yueke Hu , Emmanuel Lecouturier , Cezar Lupu
Speaker
Xavier Caruso
Time
Friday, January 7, 2022 4:00 PM - 5:00 PM
Venue
1118
Online
Zoom 638 227 8222 (BIMSA)
Abstract
Errors correcting codes are a basic primitive which provides robust tools against noise in transmission. On the theoretical perspective, they are usually founded on beautiful properties of some mathematical objects. For example, one of the oldest construction of codes is due to Reed and Solomon and takes advantage of the fact the number of roots of a polynomial cannot exceed its degree. During the last decades, new problems in coding theory have emerged (e.g. secure network transmission or distributive storage) and new families of codes have been proposed. In this perspective, Martínez- Peñas has recently introduced a linearized version of Reed-Solomon codes which, roughly speaking, is obtained by replacing classical polynomials by a noncommutative version of them called Ore polynomials. In this talk, I will revisit Martínez-Peñas' construction and give a new description of the duals of linearized Reed-Solomon codes. This will lead us to explore the fascinating world of noncommutative polynomials and notably develop a theory of residues for rational differential forms in this context.
Beijing Institute of Mathematical Sciences and Applications
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