Introduction To Algebraic Coding Theory
Book Details
Format
Hardback or Cased Book
Book Series
Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes
ISBN-10
9811220964
ISBN-13
9789811220968
Publisher
World Scientific Publishing Co Pte Ltd
Imprint
World Scientific Publishing Co Pte Ltd
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Mar 21st, 2022
Print length
268 Pages
Weight
532 grams
Dimensions
23.60 x 15.80 x 2.20 cms
Product Classification:
Algebra
Ksh 14,400.00
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We live in the age of technology where messages are transmitted in sequences of 0's and 1's through space. It is possible to make an error with noisy channels, so self-correcting codes become vital to eradicate all errors (as the number of errors is small). These self-correcting codes are widely used in the industry for a variety of applications including e-mail, telephone, remote sensing (e.g., photographs of Mars), amongst others.We will present some essentials of the theory in this book. Using linear algebra, we have the salient Hamming codes. The next level of coding theory is through the usage of ring theory, especially polynomials, rational functions and power series, to produce BCH codes, Reed-Solomon codes and the classical Goppa codes. Then we progress to the geometric Goppa code using Algebraic Geometry.
In this age of technology where messages are transmitted in sequences of 0''s and 1''s through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.
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