This note introduces the theory of
error-correcting codes to computer scientists. This theory, dating back to the
works of Shannon and Hamming from the late 40's, overflows with theorems,
techniques, and notions of interest to theoretical computer scientists. The
course will focus on results of asymptotic or algorithmic significance.
Principal topics include: Construction and existence results for
error-correcting codes, Limitations on the combinatorial performance of
error-correcting codes, Decoding algorithms, Applications in computer science.
All this said in advance so as not to anticipate the reader to refer
him to Johnny Wei Bing Lin's programming theory notes which fairly thoroughly
delivers a course on programming theory precisely tailored for management
information systems. Business data analysis begins the document which then
gradually turns into using Python as both a calculator and tool which can do
something more complex with data. Essentially, these topics include X Y plots,
simple and advanced data analyses, and text data. The notes elaborate on the
automation and management of information systems, which indicates file
management and directory organization as well as powerful program design. This
resource has been designed to equip the reader with skills practically
applicable towards efficient management and analysis of business data through
programming techniques.
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.