[PDF] Top 20 An introduction of the theory of nonlinear error-correcting codes
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An introduction of the theory of nonlinear error-correcting codes
... Vasil'yev constructed a family of nonlinear perfect codes with the same parameters as the binary. Hamming codes [6][r] ... See full document
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A Survey of the Theory of Error-Correcting Codes
... Introduction Since the very beginning of communication, there have always been errors and a need to deal with them. Human language is quite redundant, as an attempt to chat across a crackling phone line will ... See full document
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The Development of Error-Correcting Codes
... Introduction to Algebra(1/3) Finite field was invented by the early 19th century mathematician, Evariste Galois. Galois was a young French math whiz who developed a theory of finite fields, now known as ... See full document
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ERROR-CORRECTING CODES AND LATIN SQUARES
... Keywords: Error Correcting Codes, Latin Squares, Noise I INTRODUCTION Coding Theory is an important subject of study and of great mathematical ...efficient codes by which digital ... See full document
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An introduction to error correcting codes
... Reciprocally, if there are r columns linearly dependent then there are words of weight r but the minimum distance is the smallest of these weights.... Reciprocally, if there are r column[r] ... See full document
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Error Correcting Codes for Distributed Control
... about error-correcting codes that can achieve such ...of codes which under maximum likelihood decoding achieve such reliabilities and referred to them as tree ...real-time error ... See full document
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On products of linear error correcting codes
... complexity theory, briefly discussed in Section ...of codes whose squares are also asymptotically ...geometric codes that have asymptotically good higher powers, which can be constructed over large ... See full document
149
Error-correcting codes and neural networks
... the theory of error-correcting ...binary codes used by brain for encoding and storing a stimuli domain such as a rodent’s territory through the combinatorics of its covering by local ... See full document
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Capacity Achieving Forward Error Correcting Codes
... polar codes, Encoding, Decoding I. INTRODUCTION 1 Polar codes have been the subject of active research in recent times, mainly due to the fact that they are the first ever provably capacity achieving ... See full document
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Classical Error-correcting Codes in Quantum Communications
... information theory, the convergence of classical information theory and quantum theory, has produced many exciting revelations and opportunities for improving upon classical communication by ... See full document
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Implementation of reed solomon error correcting codes
... Moreover, it should be noted that no flat assumptions are made about operations like subtraction or division. These two can respectively be seen as undoing the operation, i.e. a + (-b) and a.b -1 . Other familiar ... See full document
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Error Correcting Codes for Networks, Storage and Computation
... An alternative and more appropriate way to resolve this issue is to introduce some redundancy in the data provided to the machines, in order to efficiently trade off per- machine computation time for less overall wait ... See full document
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Boolean Functions for Cryptography and Error Correcting Codes
... Such functions are of some interest to cryptography, as they allow to imple- ment in an efficient way nonlinear functions on large numbers of variables. Let us consider for example an LFSR filtered by a 63 ... See full document
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On obtaining pseudorandomness from error correcting codes
... of codes? We care to pose this question because of the numerous deep implications an answer in the affirmative holds with regard to other questions in complexity ...coding theory because it would mean that ... See full document
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Sub-class Error-Correcting Output Codes
... 1 Introduction In the literature, one can find several powerful binary ...sense, Error Correcting Output Codes were born as a general frame- work to combine binary problems to address the ... See full document
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Improved NAND Flash Memories Storage Reliability using Nonlinear Multi Error Correcting Codes
... straight codes are ...of nonlinear SEC-DED somewhat powerful codes. These codes have less imperceptible errors and less multi bit errors which are constantly miscorrected while requiring ... See full document
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Correspondence between steganographic protocols and error correcting codes
... the theory of error correcting codes, especially linear codes (see [2, ...to error correcting codes and to decoding by syndrome but the use has been ...the ... See full document
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Blockwise Repeated Burst Error Correcting Linear Codes
... I Introduction Error detecting codes and Error correcting codes have been the traditional areas of study in the field of coding techniques on error control in digital data ... See full document
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MODERATE-DENSITY BURST ERROR CORRECTING LINEAR CODES
... 1. INTRODUCTION It is well known that during the process of transmission errors occur predominantly in the form of a ...study codes which detect/correct moderate-density burst ... See full document
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Minimum distances of error correcting codes in incidence rings
... 2000 Mathematics Subject Classification: 94B60, 94B65, 16S50. It is very well known that additional algebraic structure can give advantages for coding applications. For example, all cyclic error-correcting ... See full document
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