A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
Batch Codes from Hamming and Reed-Müller Codes
[article]
2017
arXiv
pre-print
Preserved Fulltext
We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Müller codes. ...
We then show that binary first order Reed-Müller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Müller codes which have order less than ...
The REU was made possible by an NSF Research Training Group (RTG) grant (DMS #1547399) promoting Coding Theory, Cryptography, and Number Theory at Clemson. ...
arXiv:1710.07386v1
fatcat:l74bhyftonefdnlamtetk6v2ry
Batch codes from Hamming and Reed-Muller codes
2018
Journal of Algebra Combinatorics Discrete Structures and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes. ...
We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Muller codes which have order less than ...
We conclude the section by introducing a concept of optimal batch codes. After the background, we study the batch properties of binary Hamming codes and Reed-Muller codes. ...
doi:10.13069/jacodesmath.466634
fatcat:smqutqrjivhp3kkfjx2fwmovj4
Binary, Shortened Projective Reed Muller Codes for Coded Private Information Retrieval
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
These codes are obtained through homogeneous-polynomial evaluation and correspond to the binary, Projective Reed Muller (PRM) code. ...
It follows from a result by Vardy and Yaakobi, that these codes also yield optimal, systematic primitive multi-set (n, k, τ)_B batch codes for τ=3,4. ...
The restriction of evaluation to homogeneous polynomials takes us from the setting of conventional and affine RM codes to the setting of Projective Reed-Muller (PRM) codes. ...
arXiv:1702.05074v2
fatcat:g5ex7cxahrf4bm236yrgnxen6a
Page 4870 of Mathematical Reviews Vol. , Issue 2003f
[page]
2003
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
(F-LIMO-OM; Limoges) ;
de Maximy, Louis (F-LIMO-OM; Limoges)
Cyclic projective Reed-Muller codes. ...
Summary: “The projective Reed-Muller codes (PRM codes) were introduced by G. Lachaud [in Coding theory and applications (Cachan, 1986), 125-129, Lecture Notes in Comput. ...
Service Rate Region: A New Aspect of Coded Distributed System Design
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We also discover fundamental connections between multi-set batch codes and the problem of maximizing the service rate region. ...
We show the effectiveness of hybrid codes that combine replication and erasure coding in terms of code design. ...
) codes, and first-order Reed-Muller (RM) codes. ...
arXiv:2009.01598v2
fatcat:6kpn43dkmfcpdhmcj2qovkzzf4
Batch Codes from Affine Cartesian Codes and Quotient Spaces
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Affine Cartesian codes are defined by evaluating multivariate polynomials at a cartesian product of finite subsets of a finite field. In this work we examine properties of these codes as batch codes. ...
We consider the recovery sets to be defined by points aligned on a specific direction and the buckets to be derived from cosets of a subspace of the ambient space of the evaluation points. ...
This is a generalization of work in [6] , and in a similar fashion, the work in this paper aims to expand the study of batch properties from Reed-Muller codes as studied in [1] to the broader class ...
arXiv:2005.07577v1
fatcat:avy3v3lb4zdzhit5uhnclau4yy
Algebraic Coding Theory for Networks, Storage, and Security (Dagstuhl Seminar 18511)
2019
Dagstuhl Reports
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
This report documents the program and the outcomes of Dagstuhl Seminar 18511 "Algebraic Coding Theory for Networks, Storage, and Security". ...
The ever increasing traffic in networks and the growth of distributed storage systems require advanced techniques based on algebraic coding to meet user demand. ...
Consider bivariate Gabidulin "Reed-Muller" codes over general finite fields, as discussed in the working group on algebraic geometry codes. ...
doi:10.4230/dagrep.8.12.49
dblp:journals/dagstuhl-reports/ByrneBW18
fatcat:qmcdjxigx5ahxe3jpnmns4v6ka
Batch and PIR Codes and Their Connections to Locally Repairable Codes
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In this survey, two related families of codes are discussed: batch codes and codes for private information retrieval. ...
Bounds on the parameters of the codes, as well as basic constructions, are presented. Connections between different code families are discussed. ...
This work is supported in part by the grants PUT405 and IUT2-1 from the Estonian Research Council and by the EU COST Action IC1104. ...
arXiv:1611.09914v4
fatcat:qmj3i24exjcnjmuykep2h3aowq
Hardness of Approximate Nearest Neighbor Search
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Efficient PCPs from AG codes have been constructed in other settings before [BKKMS'16, BCGRS'17], but our construction is the first to yield new hardness results. ...
We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. ...
(AG) codes generalize Reed Solomon and Reed Muller codes. ...
arXiv:1803.00904v1
fatcat:7bzhtsporbadvakg5a27uh445m
KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes: each is a linear code and represents a mathematical breakthrough. ...
KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding, in the challenging short-to-medium block length regime on the AWGN channel. ...
Acknowledgements Ashok would like to thank his colleagues Mona Zehni and Konik Kothari for helpful discussions about the project. ...
arXiv:2108.12920v1
fatcat:rmv2iefpfjacxctqscacxvxaza
Reed-Muller Subcodes: Machine Learning-Aided Design of Efficient Soft Recursive Decoding
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Reed-Muller (RM) codes are conjectured to achieve the capacity of any binary-input memoryless symmetric (BMS) channel, and are observed to have a comparable performance to that of random codes in terms ...
In this paper, we focus on subcodes of RM codes with flexible rates that can take any code dimension from 1 to n, where n is the blocklength. ...
INTRODUCTION Reed-Muller (RM) codes are among the oldest families of error-correcting codes, and their origin backs to almost seven decades ago [1] , [2] . ...
arXiv:2102.01671v1
fatcat:7ycflgbs4feahgfn6g5hlypyya
Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Other Versions
This paper initiates a study of such systems within the classical coding theory. ...
Remark 4 . 8 . 48 The previous corollary on MDS codes is sharp whenever k ≤ n − k; see [7, Theorem 2].
Example 4 . 12 ( 412 First-Order Reed-Muller Code). ...
Consider the following non-systematic generator matrix G ∈ F 4×8 2 of the first order Reed-Muller code, namely
1 1 = δ 1 2 = δ 2 2 = δ 2 2 = 5 , δ 1 4 = 2 , ω 4 = 1 and δ 2 4 = 4 . 222542444 = δ 1 3 ...
arXiv:2201.07503v2
fatcat:63tvbehcwjaerfglbw5kb3yvum
Lengthening and Extending Binary Private Information Retrieval Codes
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
symbol and code extension by at most t/2 code symbols. ...
In this work, we show that a family of t-server PIR codes (with increasing dimensions and blocklengths) can be constructed from an existing t-server PIR code through lengthening by a single information ...
In the recent work of [6] , the authors found that the so-called shortened projective Reed Muller (SPRM) codes are good t-server PIR codes for t = 2 ℓ − 1 and 2 ℓ where ℓ is a positive integer. ...
arXiv:1707.03495v3
fatcat:kjd6ly2z2rarlaspeczabk4kvq
Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions
2021
Cryptography
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper. ...
This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have ...
Acknowledgments: This research work has been carried out under the leadership of the Institute for Technological Research SystemX, and therefore granted within the scope of the program "Recherche Exploratoire ...
doi:10.3390/cryptography5040038
fatcat:wkb43zunwjagbnljc6brfou4ty
Recent Progress in Code-Based Cryptography
[chapter]
2011
Communications in Computer and Information Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Section 3 deals with the new improvements of code-based signature schemes and Section 4 presents the new results in code-based secret-key cryptography. ...
The last three years have witnessed tremendous progress in the understanding of code-based cryptography. ...
Reed-Muller codes using Stern's algorithm [75] . ...
doi:10.1007/978-3-642-23141-4_3
fatcat:tydg6d5zunhbplpchcnozoaanm
« Previous
Showing results 1 — 15 out of 96 results