COLLOQUIUM Cyclic Codes Over the 2-adic Numbers Dr. Tom Blackford Department of Mathematics Western Illinois University Abstract Binary cyclic codes have been an important part of algebraic coding theory (and information theory in general) for over half a century. They have led to BCH codes and Reed-Solomon codes, which have been used in everything from transmitting satellite photos to programming CD players. Recently binary codes have been generalized to codes over integer residue rings (Z_4, Z_8, Z_9, etc.) as well as other finite rings. Very little has been written, however, about cyclic codes over infinite rings, particularly those of characteristic zero. In this talk, I will introduce the field of the 2-adic numbers, discuss cyclotomic polynomials and how X^n – 1 factors differently over different rings and fields. We will use these factorizations to classify cyclic codes over the 2-adic numbers and give some examples in which they are better than their binary counterparts of the same length. Department of Mathematics Thursday, October 28, 2010 4:00 p.m. 204 Morgan Hall Refreshments will be served at 3:45 p.m.