Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a anoisya channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sageaa free open-source mathematics software systemato illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.1.5 Venn diagram for decoding a Hamming [7, 4, 3] code and I may be identified with the above 7 A 4 matrix. ... of I, G = a a a a a 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 a a a a an , form a basis for C, i.e., G is a generator matrix.
|Title||:||Selected Unsolved Problems in Coding Theory|
|Author||:||David Joyner, Jon-Lark Kim|
|Publisher||:||Springer Science & Business Media - 2011-08-26|