Rings, Groebner Bases, and Codes

This book contains three parts. Part I provides a new proof of the fact that a finite commutative ring may be expressed as a sum of finite local rings. A Galois ring is constructed within a finite local ring by means of a Teichmuller representation system. Part II presents some variants of the Reed-Muller codes. Part III gives a standard basis for a linear code over a prime field. A decoding algorithm for binary linear codes using a Groebner basis is developed.