## USNA Pure Mathematics Seminar

The talks for the academic year 2001-2002
are held Wednesday in ** Chauvenet 201 at 3:45 pm ** unless
otherwise stated.
# Noon

**Speaker**:
#
Dr. Donald W. Newhart

##
NSA

** Title:**

#
Error-Detection Codes and Finite Fields

**Abstract**:
Finite (extension) fields have become central to many aspects
of digital communication. Actual computation in such fields requires
the equivalent of a prime number for the polynomial ring, i.e., a
specific polynomial that is irreducible over the coefficient field
(often GF(2)). This talk will begin with background on CRC's (Cyclic
Redundancy Codes) which are used for error detection, including a brief
description of the scheme which will be used in the coming GPS upgrade.
The speaker will show that this subject leads naturally to a simple,
yet common family of binary irreducible polynomials. Research at NSA
on these has led to an extension of Swan's Theorem (1962) concerning
the factor parity of trinomials.

**Time**: Noon, Wednesday Oct 17, 2001

Reception at 3:30 in the common room on the 3rd floor of Chauvenet
Hall.