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Noisy Interpolating Sets for Low Degree Polynomials

Zeev Dvir, Amir Shpilka
2008 2008 23rd Annual IEEE Conference on Computational Complexity  
As a corollary we get an explicit family of punctured Reed-Muller codes that is a family of good codes that have an efficient decoding algorithm from a constant fraction of errors.  ...  Our sets are of size O(n d ) and have efficient interpolation algorithms that can recover q from a fraction exp(−O(d)) of errors.  ...  Error correcting codes We start with the basic definitions of error correcting codes. Let F be a field and let E : F n → F m . Denote by C = E(F n ) the image of E.  ... 
doi:10.1109/ccc.2008.14 dblp:conf/coco/DvirS08 fatcat:i6vskxur2bc6zjjizr4mwvueva

Interpolation-based Chase BCH decoder

Xinmiao Zhang
2014 2014 Information Theory and Applications Workshop (ITA)  
For a (4200, 4096) BCH code, the interpolation-based Chase decoder with 16 test vectors has 2.2 times higher hardware efficiency than that based on the Berlekamp's algorithm in terms of throughput-over-area  ...  Compared to harddecision decoders, the soft-decision Chase BCH decoder can achieve significant coding gain by trying multiple test vectors.  ...  Hence, interpolation-based BCH decoding is done through considering an (n, k) t-bit error-correcting binary BCH codeword as a codeword of an (n, k ′ ) t-symbol error-correcting RS code constructed over  ... 
doi:10.1109/ita.2014.6804245 dblp:conf/ita/Zhang14 fatcat:v2opgokwijd4fli7lz4qtebbxq

List-decoding of Subspace Codes and Rank-Metric Codes up to Singleton Bound [article]

Hessam Mahdavifar, Alexander Vardy
2012 arXiv   pre-print
Subspace codes were introduced by Koetter and Kschischang to correct errors and erasures in networks where topology is unknown (the noncoherent case).  ...  The resulting error correction radius can be expressed as follows: for any integer s, our list-decoder using s+1-interpolation polynomials guarantees successful recovery of the message subspace provided  ...  Then we establish the correctness of our algorithm and compute the error correction capability of the proposed construction. A.  ... 
arXiv:1202.0866v1 fatcat:bvow3ziwk5aapkyhfbjb2db7wu

Page 556 of Mathematical Reviews Vol. 30, Issue 3 [page]

1965 Mathematical Reviews  
Author’s summary: “A method is presented for the construction of binary linear burst error correcting recurrent codes of type B2, viz., those codes which correct any burst of length /=rb or less, provided  ...  Dénes (Budapest) Preparata, Franco P. 2954 Systematic construction of optimal linear recurrent codes for burst error correction. Calcolo 1 (1964), 147-153.  ... 

Page 720 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
Summary: “In this paper, we discuss how to construct a class of generalized cyclic codes, denoted by GCC. It is well known that a cyclic code is generated by a factor of x” — 1.  ...  For this scheme, we investigate whether maximizing the guaranteed error correction rate, i.e., the number of correctable errors per transmitted symbol, necessitates pushing the code rate to zero.  ... 

Page 7009 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
Using unital modules and their automor- 94B Theory of error-correcting codes and error-detecting codes 2002i:94081 phism groups an algebraic construction of classes of perfect control schemes is given.  ...  Complexity 13 (1997), no. 1, 180-193; MR 98f:94024] we propose an efficient method for de- coding r-th order Reed-Muller codes of length 2” which can correct errors beyond half the minimum distance.  ... 

Bridging Shannon and Hamming: List Error-correction with Optimal Rate

Venkatesan Guruswami
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
Error-correcting codes tackle the fundamental problem of recovering from errors during data communication and storage. A basic issue in coding theory concerns the modeling of the channel noise.  ...  by worst-case errors. (2000) .  ...  Introduction Error-correcting codes enable reliable storage and transmission of data by providing a way to detect and rectify the errors caused by intervening noise.  ... 
doi:10.1142/9789814324359_0162 fatcat:ss7ezul2jjemhnxhnl3jjzhwzq

A Polynomial Interpolation based Quantum Key Reconciliation Protocol: Error Correction without Information Leakage [article]

Gunes Karabulut Kurt, Enver Ozdemir, Neslihan Aysen Ozkirisci, Ozan Alp Topal, Emel A. Ugurlu
2020 arXiv   pre-print
We also provide a numerical comparison of our algorithm with the asymptotic performance of the error-correcting codes and two exemplary low-density-parity-check (LDPC) codes.  ...  We provide the exact frame error rate (FER) expression of the proposed protocol. The inherent nature of the proposed algorithm ensures correcting all erroneous bits if the algorithm succeeds.  ...  More prominent key reconciliation is obtained by the utilization of the error-correcting codes (ECC).  ... 
arXiv:2004.07061v1 fatcat:au37ses56bgjtisj5vtyb4dr3m

Supplementary document for Filter construction using Ronchi masks and Legendre Polynomials to analyze the noise in aberrations applying the Irradiance Transport Equation - 4661363.pdf

Jesús Arriaga Hernández, Bolivia Otahola, Jose Oliveros, Alberto Jaramillo-Núñez, María Morín Castillo
2020 Figshare  
For the sake of our research, we have applied it to wavefronts and phases, considering this tool as a filter, to correct errors such as tilt (in both the x and y axes) in measurements performed by optical  ...  phases by analyzing not only the obtained wavefronts from irradiance measurements (such as the ITE) but also enables correcting errors and noise in Ronchigrams, Moirés, Moiré-Ronchigrams [?  ... 
doi:10.6084/m9.figshare.12482327.v5 fatcat:45pl64kvtzb6xm3hkce7n5j25i

Supplementary document for Filter construction using Ronchi masks and Legendre Polynomials to analyze the noise in aberrations applying the Irradiance Transport Equation - 4661363.pdf

Jesús Arriaga Hernández, Bolivia Otahola, Jose Oliveros, Alberto Jaramillo-Núñez, María Morín Castillo
2020 Figshare  
For the sake of our research, we have applied it to wavefronts and phases, considering this tool as a filter, to correct errors such as tilt (in both the x and y axes) in measurements performed by optical  ...  phases by analyzing not only the obtained wavefronts from irradiance measurements (such as the ITE) but also enables correcting errors and noise in Ronchigrams, Moirés, Moiré-Ronchigrams [?  ... 
doi:10.6084/m9.figshare.12482327.v4 fatcat:q6m3auviejbnjdadns6os7lppe

Page 9503 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
9503 94B Theory of error-correcting codes and error-detecting codes coordinates are transformed to binary by means of the usual Gray map and hence a+2f =n.  ...  In addition, three construction methods of constant-composition codes are presented, and a num- ber of optimum constant-composition codes are obtained by using these constructions.” 2004k:94089 94B15 Daskalov  ... 

New interpolants for asymptotically correct defect control of BVODEs

W. H. Enright, P. H. Muir
2009 Numerical Algorithms  
By employing an appropriately constructed interpolant to an approximate discrete solution to the ODE, various researchers have shown that it is possible to obtain estimates of the local error and/or the  ...  In this paper, we investigate the usefulness of asymptotically correct defect estimates for defect control in boundary value ODE (BVODE) codes.  ...  the same as those employed by the code when it uses the standard interpolant.  ... 
doi:10.1007/s11075-009-9266-3 fatcat:mq5v2dqy7rbk7lucbre564o4nq

VLSI programming for the compact disc player

Joep L.W. Kessels, Frits D. Schalij
1990 Science of Computer Programming  
Designs are derived for three error-handling functions in the compact disc player: the first decoder in the error corrector. the interpolator and the muter.  ...  The de\ipns are derived in a transformational way, which means that the ultimate design is derived by applying a series of correctness-preserving transformations on an initial design. initial designs are  ...  This subspace is the space of correct code word& A code word with at most two erroneous symbols can be corrected by projecting it onto the subspace of correct code words.  ... 
doi:10.1016/0167-6423(90)90088-u fatcat:bmxjkdlo6ncerdy6zumtozswaq

Supplementary document for Filter construction using Ronchi masks and Legendre polynomials to analyze the noise in aberrations applying the irradiance transport equation - 4661363.pdf

Jesús Arriaga Hernández, Bolivia Otahola, Jose Oliveros, Alberto Jaramillo-Núñez, María Morín Castillo
2020 Figshare  
For the sake of our research, we have applied it to wavefronts and phases, considering this tool as a filter, to correct errors such as tilt (in both the x and y axes) in measurements performed by optical  ...  phases by analyzing not only the obtained wavefronts from irradiance measurements (such as the ITE) but also enables correcting errors and noise in Ronchigrams, Moirés, Moiré-Ronchigrams [1], and others  ... 
doi:10.6084/m9.figshare.12482327.v6 fatcat:kzivdloa3zgzzkcgw4scoxycne

Supplementary document for filter construction using Ronchi masks and Legendre polynomials to analyze the noise in aberrations applying the irradiance transport equation - 4661363.pdf

Jesús Arriaga Hernández, Bolivia Otahola, Jose Oliveros, Alberto Jaramillo-Núñez, María Morín Castillo
2020 Figshare  
For the sake of our research, we have applied it to wavefronts and phases, considering this tool as a filter, to correct errors such as tilt (in both the x and y axes) in measurements performed by optical  ...  phases by analyzing not only the obtained wavefronts from irradiance measurements (such as the ITE) but also enables correcting errors and noise in Ronchigrams, Moirés, Moiré-Ronchigrams [1], and others  ... 
doi:10.6084/m9.figshare.12482327.v10 fatcat:dlt6yj4axjgrppyz3cacrnu37y
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