Codes, Curves, and Configurations of Points

Start: 09/07/2016 - 4:15pm
End  : 09/07/2016 - 5:15pm


Nathan Kaplan (UCI)


We give an introduction to error-correcting codes focusing on connections to combinatorics, linear algebra, and geometry.  No previous familiarity with coding theory will be assumed. 

A code C is a subset of (F_q)^n, where F_q denotes the finite field of q elements.  The Hamming distance between two elements of (F_q)^n is the number of coordinates in which they are different.  For fixed q and n what is the maximum size of a code such that any two of its elements have Hamming distance at least d?  This problem is easy to state but leads to surprisingly complicated mathematics.  We will focus on one extremal family, the Maximum Distance Separable (MDS) codes.  Understanding these codes (when they exist, how many there are, etc.) is a major problem in coding theory that has natural connections to classical algebraic geometry.

Kravis Center Lower Court 62, Claremont McKenna College

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