This book explains the following topics: Linear Codes, Probability
as Fancy Counting and the q-ary Entropy Function, Combinatorics, The Greatest
Code of Them All: Reed-Solomon Codes, What Happens When the Noise is Stochastic:
Shannon's Theorem, Bridging the Gap Between Shannon and Hamming: List Decoding,
Code Constructions, Code Concatenation, Algorithms, Decoding Concatenated Codes,
Efficiently Achieving the Capacity of the BSCp, Efficient Decoding of
Reed-Solomon Codes, Efficiently Achieving List Decoding Capacity, Applications.
Author(s): Venkatesan Guruswami, Atri Rudra and Madhu
Sudan
Kenneth Leroy Busbee and Dave Braunschweig's Programming
Fundamentals is a book that offered readers a more solid foundation in
programming concepts. The text covers the basic elements of programming systems:
from data types to the operators and the functions, to control structures
including the conditions and the loops, advanced elements such as arrays and
strings processing files among others. The book focuses on object-oriented
programming and brings out classes and objects. This material is widely used by
students looking to develop a solid foundation of programming principles and
practices-a growing emphasis on practical application and theoretical
knowledge.
Author(s): Kenneth Leroy Busbee, Dave
Braunschweig
This comprehensive note
considers some basic material in coding theory and discusses sphere packing and
Shannon's theorem, which form the basics to understanding the idea of error
correction and data transmission. It also deals with the concept of linear codes
and their applications by describing Hamming codes and generalized Reed-Solomon
codes. The material further takes a look at some codes within the frameworks of
modifiation of codes and codes over subfields, providing insights into cyclic
codes. Furthermore, it addresses the importance of countering weights and
distances in error-correcting codes, thus making it a very vital text for
students and professionals looking to deepen their knowledge on mathematical
underpinnings and practical applications of coding theory.