Advisor:  John Lowengrub

Abstract:  In Many types of modern communication, a message is transmitted over a noisy medium.  This creates a chance that the message will become corrupted.  The purpose of an error-correcting code is to add some redundant information to the message which allows the receiver to detect and correct those errors accrued during the transmission.  In this talk, we will study the famous Reed-Solomon code (found in QR codes, compact discs, deep space probes,...) and consider it's error-correcting capacity.  This will lead us to studying the "deep-hole" problem, which is a question of determining when a received message has, in a sense,  incurred the worst possible corruption.  It is a new and important problem that could give insight on finding the upper bound for the  error-correcting capacity of the Reed-Solomon code.
Advisor:  Professor Daqing Wan

Advisor: Natalia Komarova

Advisor: Long Chen

Advisor: Vladimir Baranovsky