- Bit by Bit: Binary codes and algorithms for text compression and error detection

2014 ◽  
pp. 266-305
2021 ◽  
Vol 19 (2) ◽  
pp. 140-143
Author(s):  
A. Yu. Matrosova

Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes. Vol. 1. Moscow, Nauka publ., 2020, 611 p. ISBN 978-5-02-040758-9.Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes. Vol. 2. Moscow, Nauka publ., 2021, 527 p. ISBN 978-5-02-040757-2.The first volume of the book includes papers devoted to three main areas of research in the field of synthesis of self-checking discrete systems: study of features of classical sum codes (Berger codes), modular sum codes, as well as their modifications proposed by the authors of the articles; study of features of codes for which check bits are obtained using convolutions modulo М = 2 of a part of data bits (polynomial codes and classical Hamming codes); research of the Boolean Complement method for organisation of self-checking discrete systems based on redundant binary codes. Materials are provided on detailed characteristics of error detection in data bits of redundant binary codes under the condition of errorfree check bits, descriptions of methods for constructing previously unknown modified sum codes and features of methods for synthesizing self-checking discrete systems based on binary redundant codes.The second volume of the book includes papers in the field of constructing binary sum codes weighted bits and transitions between bits occupying adjacent positions in data vectors of code words, as well as the results of studying their characteristics and methods of synthesising coding equipment. The issues of application of features of codes in organisation of self-checking discrete systems are considered. The reader will find on the pages of this volume materials on detailed characteristics of error detection in data bits of weight-based sum codes provided that the check bits are error-free, descriptions of methods for constructing previously unknown weight-based sum codes and features of methods for synthesising self-checking discrete systems based on them.The book can be useful for developers, researchers and engineers working in the field of technical diagnostics of discrete systems and synthesis of systems with fault detection, as well as students studying computer science, computer technology and automation. 


2018 ◽  
Vol 18 (5) ◽  
pp. 63-76
Author(s):  
Alexander A. Davydov ◽  
Stefano Marcugini ◽  
Fernanda Pambianco

Abstract Binary codes created by doubling construction, including quasi-perfect ones with distance d = 4, are investigated. All [17·2r−6, 17·2r−6 − r, 4] quasi-perfect codes are classified. Weight spectrum of the codes dual to quasi-perfect ones with d = 4 is obtained. The automorphism group Aut(C) of codes obtained by doubling construction is studied. A subgroup of Aut(C) is described and it is proved that the subgroup coincides with Aut(C) if the starting matrix of doubling construction has an odd number of columns. (It happens for all quasi-perfect codes with d = 4 except for Hamming one.) The properness and t-properness for error detection of codes obtained by doubling construction are considered.


1993 ◽  
Author(s):  
Cleopas Angaye ◽  
Paul Fisher
Keyword(s):  

2020 ◽  
Author(s):  
Xingxing Wu ◽  
Reto M. Witzig ◽  
Rodolphe Beaud ◽  
Christian Fischer ◽  
Daniel Häussinger ◽  
...  

Governing higher-order stereogenicity is a long-standing goal in stereoselective catalysis, because it allows to achieve selectivity for more than a twofold number of stereoisomers per stereogenic unit. Current methods warrant control over the power of two stereoisomers and the configurations are routinely assigned using the descriptors ( R ) and ( S ), or related binary codes. In contrast, conformational analysis ranges beyond this dualistic treatment of stereoisomerism, which constitutes an unmet challenge for catalyst stereocontrolled processes. Herein, we now report that sixfold stereogenicity can be governed by stereoselective catalysis. By controlling a configurationally stable stereogenic axis with six large rotational barriers, a catalytic [2+2+2]-cyclotrimerization selectively governs the formation of one out of six stereoisomers with up to 0:0:2:98:0:0 stereocontrol. The underpinnings of conformational analysis and stereoselective catalysis are thereby conceptually reunited. Novel molecular architectures featuring distinct chemical topologies and unexplored chemical designs are anticipated from catalystcontrol over higher-order stereogenicities


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