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On complete decoding of linear error-correcting codes

David M. Mandelbaum
1980 Information and Control  
It is shown that minimum distance decoding of linear codes is accomplished by generating all codewords corresponding to all information sets utilizing the corresponding received coordinates.  ...  This was previously shown for the special case of maximum distance separable codes.  ...  COMPLETE DECODING OF LINEAR CODES Consider an (n, k) linear code C. Let y be a received vector such that y = .Y + e, where )7 is a member of C and e is any noise vector that is not a member of C.  ... 
doi:10.1016/s0019-9958(80)90526-4 fatcat:arlrmfchfrbhtf7dcbbtrovoma

The simplification of computationals in error correction coding

Vasyl Semerenko, Oleksandr Voinalovich
2021 Technology Audit and Production Reserves  
Correction of single errors during one time interval (one iteration) of decoding has a linear decoding complexity on the length of the codeword, and error correction during m iterations of permutations  ...  The mathematical apparatus of linear automata allows solving together the indicated problems of error correction coding.  ...  A sign of correct decoding is obtaining a zero value of the error syndrome S err at one of the iterations. Let's estimate the complexity of decoding using cyclic permutations.  ... 
doi:10.15587/2706-5448.2021.233656 fatcat:q4s5obslyvehtefysbt6qq4flu

Book announcements

1993 Discrete Applied Mathematics  
Chapter 8: Linear codes. codes and other modifications. Simultaneous correction and detection of errors. Mac Williams identity. Chapter 9: Reed-Muller Codes: Weak Codes with Easy Decoding.  ...  Extended Fast Decoding of BCH Codes. Error location and error evaluation. Euclidean algorithm. The decoding algorithm. Chapter 14: Convolutional Codes.  ...  Special types of goal orientation. Chapter 11: Systems Science in Retrospect and Prospect. Criticism. Status and impact of systems science. The future of systems science.  ... 
doi:10.1016/0166-218x(93)90039-q fatcat:dzfjtre6sbb4lpjhoxzef7umvy

Error Detection and Correction Using Hamming and Cyclic Codes in a Communication Channel

Irene Ndanu John
2016 Pure and Applied Mathematics Journal  
We have generated, encoded and decoded these codes as well as schemes and/or algorithms of error-detecting and error-correcting of these codes.  ...  This paper provides an overview of two types of linear block codes: Hamming and cyclic codes.  ...  Acknowledgements The authors wish to thank Taita Taveta University for the support given towards the completion of this research. Special thanks goes to the Department of Mathematics and Informatics.  ... 
doi:10.11648/j.pamj.20160506.17 fatcat:z3vei2wvhvez3afkvodg4ua6y4

Page 3919 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
Several classes of linear block codes are proved to have good error-detecting capability.” 841:94034 Lu, Shao Hua 84i:94035 The generalized BCH code and its error-correcting capacity. (Chinese.  ...  Authors’ summary: “The probability of undetected error of linear block codes for use on a binary symmetric channel is investigated. Upper bounds are derived.  ... 

Implementation of burst-correcting convolutional codes

J. Massey
1965 IEEE Transactions on Information Theory  
A block diagram of a complete decoder is given for an optimal burstcorrecting code.  ...  The decoding procedure can then be implemented with a circuit of the same order of complexity as a parity-checking circuit for a block-linear code.  ...  Gallager at Codex Corporation during the course of the research for this paper.  ... 
doi:10.1109/tit.1965.1053798 fatcat:j4r26fnycndcdlxkhdace553im

Linear-Time Encodable/Decodable Codes With Near-Optimal Rate

V. Guruswami, P. Indyk
2005 IEEE Transactions on Information Theory  
We present an explicit construction of linear-time encodable and decodable codes of rate r which can correct a fraction (1 − r − ε)/2 of errors over an alphabet of constant size depending only on ε, for  ...  The error-correction performance of these codes is optimal as seen by the Singleton bound (these are "near-MDS" codes).  ...  Acknowledgments We would like to thank the anonymous referees and Jørn Justesen for useful comments on the presentation.  ... 
doi:10.1109/tit.2005.855587 fatcat:2d2h7z62bjafdgcooj26ulomla

On Z/sub 4/- and Z/sub 9/-linear lifts of the Golay codes

M. Greferath, E. Viterbo
1999 IEEE Transactions on Information Theory  
We analyze 4 -and 9 -linear lifts of the binary [24; 12] and ternary [12; 6]-Golay code under different weight functions on the underlying ring, and present algebraic decoding schemes for these codes.  ...  For the characterization of the errors being corrected we adopt the notation of [10] defining the type of a word e as its (complete) enumerator.  ...  A Decoder for Ep and a Set of Permutations Complete algebraic decoders for the cyclic Golay codes have been developed in [5] and [6] .  ... 
doi:10.1109/18.796396 fatcat:flqgvwvo7vax5fsmeaop5kuazu

MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes

Rafael Misoczki, Jean-Pierre Tillich, Nicolas Sendrier, Paulo S. L. M. Barreto
2013 2013 IEEE International Symposium on Information Theory  
Basically, the security of the McEliece cryptosystem is based on two assumptions: the pseudo-randomness of the employed code family and the hardness of decoding a generic linear code.  ...  The private code has an error correction capability very close to mt, whilst the public code has an error correction capability much higher than t. 2.  ...  Basically, the security of the McEliece cryptosystem is based on two assumptions: the pseudo-randomness of the employed code family and the hardness of decoding a generic linear code.  ... 
doi:10.1109/isit.2013.6620590 dblp:conf/isit/MisoczkiTSB13 fatcat:hkeuja3b6rhgtm3xruezsfx244

Use of Linear Error-Correcting Subcodes in Flow Watermarking for Channels with Substitution and Deletion Errors [chapter]

Boris Assanovich, William Puech, Iuliia Tkachenko
2013 Lecture Notes in Computer Science  
The evaluation of scheme demonstrates similar to known scheme performance but with lower complexity as soon as its implementation is mainly based on linear decoding operations.  ...  An invisible flow watermarking QIM scheme based on linear errorcorrecting subcodes for channels with substitution and deletion errors is proposed in this paper.  ...  The error correction capacity t of linear error-correcting codes strictly depends on its minimum distance d min =min{d(x i ;x j )} and weight distribution of a code.  ... 
doi:10.1007/978-3-642-40779-6_8 fatcat:eeuzudpw2jakrfwz3ly2iyfala

The variant of post-quantum cryptosystem based on burst-correcting codes and on the complete decoding problem

Andrey Ovchinnikov
2022 Information and Control Systems  
An important direction here is code-based cryptography utilizing the mathematical problems from error-correcting coding theory.  ...  The cryptocomplexity of the system is supposed to be based on the complete decoding problem, which is believed to be a harder mathematical problem than those used in existing systems.  ...  The variant of post-quantum cryptosystem based on burst-correcting codes and on the complete decoding problem.  ... 
doi:10.31799/1684-8853-2022-3-45-54 fatcat:v72cmmjp3bbjbbc5kpeskiee3q

Page 2483 of Mathematical Reviews Vol. , Issue 80F [page]

1980 Mathematical Reviews  
Author’s summary: “A class of easily decodable, highly efficient, burst-error-correcting linear ((2”—1)/m, (2"—3)im) codes is de- scribed. These codes correct bursts of length b > (/—0.5)m, where !  ...  A complete list of CF(2, 5) codes.  ... 

Modified majority logic decoding of cyclic codes in hybrid-ARQ systems

M.D. Rice, S.B. Wicker
1992 IEEE Transactions on Communications  
Reliability information provided by sets of orthogonal check sums in a majority logic decoder for block codes is used in a type-I hybrid ARQ error control scheme.  ...  It is shown that the reliability performance of Reed-Muller and other majority logic decodable codes can be substantially improved at the expense of a very small reduction in throughput.  ...  In general, a given ( 7 1 . k ) linear block code can detect at least twice as many errors per received word as it can correct using complete decoding.  ... 
doi:10.1109/26.163560 fatcat:uvl4wzymlnaujeubs44z4adj3q

Page 4388 of Mathematical Reviews Vol. , Issue 86i [page]

1986 Mathematical Reviews  
K. (1-LEHI) On quasiperfect property of double-error-correcting Goppa codes and their complete decoding. Inform. and Control 61 (1984), no. 2, 132-146.  ...  These last two are new extremal ternary codes. Vera Pless (Chicago, Ill.) Elia, Michele (I-TRNP); Prati, Gianfranco 861:94065 (I-TRNP) On the complete decoding of binary linear codes. IEEE Trans.  ... 

Block Network Error Control Codes and Syndrome-based Complete Maximum Likelihood Decoding [article]

Hossein Bahramgiri, Farshad Lahouti
2008 arXiv   pre-print
Specifically, it is shown that using the proposed syndrome-based complete decoding, a network error correcting code with redundancy order d for receiver t, can correct d-1 random additive errors with a  ...  The block network error control coding framework, BNEC, is presented and the capability of the scheme to correct a mixture of symbol errors and packet erasures and to detect symbol errors is studied.  ...  In [19] , minimum distance for linear network codes is presented and based on which, the capability of a network code for error correction, error detection and erasure correction is characterized.  ... 
arXiv:0809.4149v1 fatcat:p56n4ex6n5fhnghg3lfscq4bvy
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