The Set Codes PDF Download
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Author: G. G. Bilodeau
Publisher:
ISBN:
Category : Structural analysis (Engineering)
Languages : en
Pages : 34
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Book Description
Author: G. G. Bilodeau
Publisher:
ISBN:
Category : Structural analysis (Engineering)
Languages : en
Pages : 34
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Book Description
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1599730790
Category : Computers
Languages : en
Pages : 169
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Book Description
This book provides, for the first time, a few classes of Set Codes, the most generalized class of algebraic codes.These codes are best-suited for their applications in cryptography, coding block truncation, image compression, computer networking and data storage.
Author: Cunsheng Ding
Publisher: World Scientific
ISBN: 981461937X
Category : Mathematics
Languages : en
Pages : 354
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Book Description
This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes. This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.
Author: Mumtaz Ali
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 10
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Book Description
In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example.
Author: Abhijit Dasgupta
Publisher: Springer Science & Business Media
ISBN: 1461488540
Category : Mathematics
Languages : en
Pages : 434
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Book Description
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Author: Nicola O’Brien
Publisher: CSIRO PUBLISHING
ISBN: 1486312365
Category : Science
Languages : en
Pages : 120
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Book Description
Are you ready to learn about real technology and make it yourself? Ready, Set, Code! explains how cutting-edge digital technology works and its surprising uses now and in the future. Filled with interesting examples, each chapter explores a different topic, such as artificial intelligence, sensors and data, and applies it with a fun, hands-on coding project. You will learn how to create your own chatbot, translate messages into different languages, construct a burglar alarm, make digital art and music, and launch a citizen science project. Plus, you’ll learn how to protect yourself online and much more. Suitable for beginners, this book provides illustrated step-by-step instructions to teach kids to code with the highly acclaimed Scratch programming language, popular micro:bit mini computers and simple app building tools.
Author: Ian F. Blake
Publisher: Academic Press
ISBN: 1483260593
Category : Mathematics
Languages : en
Pages : 369
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Book Description
The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.
Author: Ian F. Blake
Publisher: Cambridge University Press
ISBN: 1009283375
Category : Computers
Languages : en
Pages : 473
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Book Description
Brief informal introductions to coding techniques developed for the storage, retrieval, and transmission of large amounts of data.
Author: Valery Sklyarov
Publisher: Springer Science & Business Media
ISBN: 3319047086
Category : Technology & Engineering
Languages : en
Pages : 443
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Book Description
The book is composed of two parts. The first part introduces the concepts of the design of digital systems using contemporary field-programmable gate arrays (FPGAs). Various design techniques are discussed and illustrated by examples. The operation and effectiveness of these techniques is demonstrated through experiments that use relatively cheap prototyping boards that are widely available. The book begins with easily understandable introductory sections, continues with commonly used digital circuits, and then gradually extends to more advanced topics. The advanced topics include novel techniques where parallelism is applied extensively. These techniques involve not only core reconfigurable logical elements, but also use embedded blocks such as memories and digital signal processing slices and interactions with general-purpose and application-specific computing systems. Fully synthesizable specifications are provided in a hardware-description language (VHDL) and are ready to be tested and incorporated in engineering designs. A number of practical applications are discussed from areas such as data processing and vector-based computations (e.g. Hamming weight counters/comparators). The second part of the book covers the more theoretical aspects of finite state machine synthesis with the main objective of reducing basic FPGA resources, minimizing delays and achieving greater optimization of circuits and systems.
Author: Jean-Guillaume Dumas
Publisher: John Wiley & Sons
ISBN: 1118960866
Category : Computers
Languages : en
Pages : 388
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Book Description
Offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations This book offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations. This text focuses on the ways to structure information so that its transmission will be in the safest, quickest, and most efficient and error-free manner possible. All coding operations are covered in a single framework, with initial chapters addressing early mathematical models and algorithmic developments which led to the structure of code. After discussing the general foundations of code, chapters proceed to cover individual topics such as notions of compression, cryptography, detection, and correction codes. Both classical coding theories and the most cutting-edge models are addressed, along with helpful exercises of varying complexities to enhance comprehension. Explains how to structure coding information so that its transmission is safe, error-free, efficient, and fast Includes a pseudo-code that readers may implement in their preferential programming language Features descriptive diagrams and illustrations, and almost 150 exercises, with corrections, of varying complexity to enhance comprehension Foundations of Coding: Compression, Encryption, Error-Correction is an invaluable resource for understanding the various ways information is structured for its secure and reliable transmission in the 21st-century world.
