Abstract: We show how Grobner basis theory can be used in coding
theory, especially in the construction and decoding of linear codes.
A new method is given for construction of a large class of linear codes
that has a natural decoding algorithm. It works for any finite field
and any block length. The codes constructed include as special cases
many of the well known codes such as Reed-Solomon codes, Hermitian
codes and, more generally, all one-point algebraic geometry codes.
This method also allows us to construct random codes for which
our decoding algorithm performs reasonably well. Joint work with
Jeffrey B. Farr.