This note covers
the following topics: Functions, Values and Side Effects, Control and
Higher-Order Functions, Environments and Lambda, Newton's Method and Recursion,
Data Abstraction, Sequences and Iterables, Objects, Lists, and Dictionaries,
Mutable Data Types, Object-Oriented Programming, Inheritance, Generic Functions,
Coercion and Recursive Data, Functional Programming, Declarative Programming,
Unification, MapReduce, Parallelism.
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.
This book is meant for
undergraduate students who wish to obtain a basic knowledge in coding theory
based on the subject of linear codes. It begins with introductory chapters based
on Shannon theory and relevant to coding, then advances to detailed discussions
about decoding linear codes and the MacWilliams identity. Besides these, the
construction of new codes and the attainment of bounds on code performance are
subjects of discussion, and thus Reed-Muller codes prove very significant in
this light. This book is an exposition of the practical coding theory applied in
many fields: telecommunications to data storage. It focuses on fast decoding
techniques and higher-order RM codes.