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.