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1Computational Complexity Of Bilinear Forms : Algebraic Coding Theory And Applications Of Digital Communication Systems

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2Microsoft Research Audio 104585: Coding Theory: Survey Of Recent Progress And Open Questions

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Coding theory emerged in the late 1940's, thanks to the works of Shannon and Hamming, as the theory supporting 'reliable transmission of information (in the presence (fear?) of noise)'. More than fifty years since, enormous progress has been made within this theory. At the same time, some of the most central questions remain mysteriously elusive. In this talk we will survey some recent progress, (hopefully) clarify some of the (pervasive?) misconceptions, and lay out some of the classical questions that remain open. ©2005 Microsoft Corporation. All rights reserved.

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3Information Theory And Coding

Coding theory emerged in the late 1940's, thanks to the works of Shannon and Hamming, as the theory supporting 'reliable transmission of information (in the presence (fear?) of noise)'. More than fifty years since, enormous progress has been made within this theory. At the same time, some of the most central questions remain mysteriously elusive. In this talk we will survey some recent progress, (hopefully) clarify some of the (pervasive?) misconceptions, and lay out some of the classical questions that remain open. ©2005 Microsoft Corporation. All rights reserved.

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4URSI National Committee Report: Commission 6. Radio Waves And Circuits. Part 1. Information Theory And Coding

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Journal of Research of the National Bureau of Standards

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5Syllabus For A Coding Theory Course (2005/6)

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Syllabus of Coding Theory course 2005/2006 second semistet by KIT

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6Coding Theory Projection: Group, Field, Finite Field

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Projection from a course on Coding Theory (2005 - 6) by KIT

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7Coding Theory Lecture : Group, Polynomial, And Hamming Codes

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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8Coding Theory Projection: Finite Field- And BCH Codes

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Projection from a course on Coding Theory (2005 - 6) by KIT

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9Coding Theory Lecture: Cryptography

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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10ICD-10-CM/PCS Coding : Theory And Practice

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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11Modified Evidence Coding Method Based On Dezert-Smarandache Theory

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The calculation is an important issue which affects the application of the Dezert-Smarandache Theory (DSmT). The research of the calculation is a hotspot in the area of the DSmT. The calculation code is widely recognized for the reasonability of evidence expression and belief computation. The calculation code is simple and effective in the coding process.

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12Coding Theory Projection: Bounds

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Projection from a course on Coding Theory (2005 - 6) by KIT

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13Coding Theory Projection: Finite Field- And BCH Codes

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Projection from a course on Coding Theory (2005 - 6) by KIT

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14Coding Theory Projection: Linear Codes

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Projection from a course on Coding Theory (2005 - 6) by KIT

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15Coding Theory Lecture: Cyclic Codes

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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16Coding Theory Exercise: Error And Distance

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Exercises from a course on Coding Theory (2005 - 6) by KIT

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17A First Course In Coding Theory

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Exercises from a course on Coding Theory (2005 - 6) by KIT

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18ERIC ED096337: Coding Occupations According To Holland's Vocational Theory.

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The revision of the Strong Vocational Interest Blank (SVIB), the Strong-Campbell Interest Inventory (SCII), introduces Holland's theory of occupational types into the empirical structure of the SVIB. Emphasis on Holland's theory is evident throughout the SCII profile. Empirical coding of occupations was accomplished by: (1) scoring each of the occupational samples on the Holland scales; (2) correlating the Occupational Scales, the Basic Interest Scales, and the General Occupational Theme Scales; and (3) typing each occupation according to its highest General Theme scores while simultaneously considering the scale intercorrelations. The coded occupations were ordered on the new SCII profile in congruence with Holland's hexagonal model--Realistic, Investigative, Artistic, Social, Enterprising, and Conventional. Most of the Occupational Scales ordered themselves around the perimeter of the hexagon according to Holland's theory. Occasionally, occupations fell into unusual categories, emphasized differences in code-types for men and women, or resisted easy categorization. The exploration of these unusual occurrences is useful for counselors and clients who wish to gain more information about vocational interests. (Author/RC)

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19CODING THEORY AND ITS APPLICATIONS TO COMMUNICATIONS SYSTEMS LEONARD BAULERT,

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Coding theory applications to communications systems - code correlations, pseudorandom coded ranging system, coded phase-coherent communication

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20Introduction To Coding Theory

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Coding theory applications to communications systems - code correlations, pseudorandom coded ranging system, coded phase-coherent communication

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21ICD-9-CM Coding : Theory And Practice With ICD-10

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Coding theory applications to communications systems - code correlations, pseudorandom coded ranging system, coded phase-coherent communication

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22Key Papers In The Development Of Coding Theory

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Coding theory applications to communications systems - code correlations, pseudorandom coded ranging system, coded phase-coherent communication

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23Information Theory : Coding Theorems For Discrete Memoryless Systems

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452p. ; 25cm

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24A Review Of Coding Theory

A Review Of Coding Theory

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25ERIC ED218084: Aspects Of Coding. Applications Of Linear Algebra To Communication And Information Science. [and] A Double-Error Correcting Code. Applications Of Algebra To Information Theory. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 336 And 337.

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These two modules cover aspects of the coding process and algebraic coding theory. The first unit defines coding as a branch of information and communication science, which draws extensively upon many diverse mathematical fields, primarily abstract and linear algebra, number theory, probability and statistics, and combinatorial theory. Aspects of the process, including linear codes and error correction, are discussed. The second unit focuses on the construction of a double-error correcting code. Both units contain problems and answers to these exercises. The second unit contains a model exam and concludes with an answer key to this test. (MP)

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  • Title: ➤  ERIC ED218084: Aspects Of Coding. Applications Of Linear Algebra To Communication And Information Science. [and] A Double-Error Correcting Code. Applications Of Algebra To Information Theory. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 336 And 337.
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“ERIC ED218084: Aspects Of Coding. Applications Of Linear Algebra To Communication And Information Science. [and] A Double-Error Correcting Code. Applications Of Algebra To Information Theory. Modules And Monographs In Undergraduate Mathematics And Its Applications Project. UMAP Units 336 And 337.” Subjects and Themes:

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26Coding Theory Lecture: Finite Field- And BCH Codes

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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27Coding Theory Example: Linear Codes

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Examples from a course on Coding Theory (2005 - 6) by KIT

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28Coding Theory Lecture: Goppa Codes

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Lecture from a course on Coding Theory (2005 - 6) by KIT

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29Coding Theory Exercise: Group, Polynomial, And Hamming Codes

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Exercises from a course on Coding Theory (2005 - 6) by KIT

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30ETM 2126 - Information Theory And Error Control Coding

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Trimester 2 - 2019/2020

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31Coding Theory : A First Course

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Trimester 2 - 2019/2020

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32Imagery And Text : A Dual Coding Theory Of Reading And Writing

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Trimester 2 - 2019/2020

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33Coding Theory Projection: Group, Polynomial, And Hamming Codes

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Projection from a course on Coding Theory (2005 - 6) by KIT

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34Coding And Information Theory

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35Coding Theory And Algebraic Geometry : Proceedings Of The International Workshop Held In Luminy, France, June 17-21, 1991

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36Coding Theory And Design Theory

Projection from a course on Coding Theory (2005 - 6) by KIT

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37ETM 2126 - Information Theory And Error Control Coding

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Trimester 2 - 2016/2017

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38The Mathematics Of Coding Theory : Information, Compression, Error Correction, And Finite Fields

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Trimester 2 - 2016/2017

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39Source Coding Theory

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Includes bibliographical references (p. 177-183)

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40ETM 2126 - Information Theory And Error Control Coding

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Tri 2 2022/2023

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41The Mathematical Theory Of Coding

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Tri 2 2022/2023

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42Modern Coding Theory: The Statistical Mechanics And Computer Science Point Of View

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These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory, highlighting connections with statistical mechanics. We also stress common concepts with other disciplines dealing with similar problems that can be generically referred to as `large graphical models'. While most of the lectures are devoted to the classical channel coding problem over simple memoryless channels, we present a discussion of more complex channel models. We conclude with an overview of the main open challenges in the field.

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43ICD-9-CM Coding, 2011 Edition - Text And Workbook Theory And Practice

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44Introduction To Coding Theory

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45DTIC AD0401924: STUDY ON APPLICATION OF CODING THEORY

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Digital codes and finite state machines.

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46Some Applications Of Coding Theory In Computational Complexity

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Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs.

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47Arithmetic, Geometry, And Coding Theory : Proceedings Of The International Conference Held At Centre International De Rencontres Mathématiques (CIRM), Luminy, France, June 28-July 2, 1993

Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs.

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48Coding Theory And Projective Spaces

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The projective space of order $n$ over a finite field $\F_q$ is a set of all subspaces of the vector space $\F_q^{n}$. In this work, we consider error-correcting codes in the projective space, focusing mainly on constant dimension codes. We start with the different representations of subspaces in the projective space. These representations involve matrices in reduced row echelon form, associated binary vectors, and Ferrers diagrams. Based on these representations, we provide a new formula for the computation of the distance between any two subspaces in the projective space. We examine lifted maximum rank distance (MRD) codes, which are nearly optimal constant dimension codes. We prove that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. The incidence matrix of the transversal design derived from a lifted MRD code can be viewed as a parity-check matrix of a linear code in the Hamming space. We find the properties of these codes which can be viewed also as LDPC codes. We present new bounds and constructions for constant dimension codes. First, we present a multilevel construction for constant dimension codes, which can be viewed as a generalization of a lifted MRD codes construction. This construction is based on a new type of rank-metric codes, called Ferrers diagram rank-metric codes. Then we derive upper bounds on the size of constant dimension codes which contain the lifted MRD code, and provide a construction for two families of codes, that attain these upper bounds. We generalize the well-known concept of a punctured code for a code in the projective space to obtain large codes which are not constant dimension. We present efficient enumerative encoding and decoding techniques for the Grassmannian. Finally we describe a search method for constant dimension lexicodes.

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49A Coding Theory Foundation For The Analysis Of General Unconditionally Secure Proof-of-retrievability Schemes For Cloud Storage

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There has been considerable recent interest in "cloud storage" wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover or retrieve the file given any "proving algorithm" that has a sufficiently high success probability. This paper treats proof-of-retrievability schemes in the model of unconditional security, where an adversary has unlimited computational power. In this case retrievability of the file can be modelled as error-correction in a certain code. We provide a general analytical framework for such schemes that yields exact (non-asymptotic) reductions that precisely quantify conditions for extraction to succeed as a function of the success probability of a proving algorithm, and we apply this analysis to several archetypal schemes. In addition, we provide a new methodology for the analysis of keyed POR schemes in an unconditionally secure setting, and use it to prove the security of a modified version of a scheme due to Shacham and Waters under a slightly restricted attack model, thus providing the first example of a keyed POR scheme with unconditional security. We also show how classical statistical techniques can be used to evaluate whether the responses of the prover are accurate enough to permit successful extraction. Finally, we prove a new lower bound on storage and communication complexity of POR schemes.

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50Lattice Polytopes In Coding Theory

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In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.

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  • Title: ➤  Lattice Polytopes In Coding Theory
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