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# ALGEBRAIC CODING THEORY

Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels. It makes use of classical and modern algebraic techniques involving finite fields, group theory, and polynomial algebra. It has connections with other areas of discrete mathematics, especially number theory and the theory of experimental designs. Codes are used for data compression, cryptography, error-correction and more recently also for network coding. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction (or detection) of errors in the transmitted data. Algebraic coding theory gives an introduction to the exciting field of coding theory. In first chapter, elementary techniques of algebraic coding theory are here used to discuss the three biplanes with k=6. These three designs are intimately related to the (16, 11) extended binary Hamming code and to one another; we systematically investigate these relationships. We also exhibit each of the three designs as difference sets. Second chapter focuses on the most weight w vectors in a dimension k binary code. In third chapter, a statistical recognition method of the binary BCH code is proposed. Fourth chapter presents an introduction to algebraic coding theory. Fifth chapter proposes a solution to blind recognition of binary cyclic codes. Sixth chapter is concerned with the computation of the lower bounds for third-order nonlinearities of two classes and seventh chapter discusses on third-order nonlinearity of biquadratic monomial Boolean functions. Eighth chapter presents on the class of perfect nonlinear polynomial functions and ninth chapter presents an overview on the computing of the minimum distance of
Editora: MAGNUM PUBLISHING
ISBN: 9781682503010
ISBN13: 9781682503010
Edição: 1ª Edição - 2016
Número de Páginas: 208
Acabamento: HARDCOVER
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