Rings, Groebner Bases, and Codes

By Vololona Harinoro Rakotomalala and Harinaivo Andriatahiny

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.

• Format: Paperback
• Language: English
• ISBN: 620552953X
• ISBN13: 9786205529539
• Release Date: December 2022
• Publisher: LAP Lambert Academic Publishing
• Length: 88 Pages
• Weight: 0.31 lbs.
• Dimensions: 0.2" x 6.0" x 9.0"