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Generalized subspace subcodes with application in cryptology [article]

Thierry P. Berger, Cheikh Thiécoumba Gueye, Jean Belo Klamti
2017 arXiv   pre-print
They are obtained by taking equivalent codes, for example the generalized Reed Solomon codes, or by using the so-called subfield subcode method, which leads to Alternant codes and Goppa codes over the  ...  The main advantages of these constructions is to preserve both the minimum distance and the decoding algorithm of the underlying Reed Solomon code.  ...  We propose to use generalized subspace subcodes of Reed-Solomon codes (GSS codes of GRS codes for short).  ... 
arXiv:1704.07882v1 fatcat:c5sokhd2gfdmjh2qpx6nq6pv64

Reducing Key Length of the McEliece Cryptosystem [chapter]

Thierry P. Berger, Pierre-Louis Cayrel, Philippe Gaborit, Ayoub Otmani
2009 Lecture Notes in Computer Science  
Starting from subfield subcodes of quasi-cyclic generalized Reed-Solomon codes, we propose a system with several size of parameters from 6,000 to 11,000 bits with a security ranging from 2 80 to 2 107  ...  Our construction introduces a new method of hiding the structure of the secret generator matrix by first choosing a subfield subcode of a quasi-cyclic code that is defined over a large alphabet and then  ...  This attack can be used against any type of generalized Reed-Solomon code but uses the fact that the underlying matrix of the Reed-Solomon code is completely known.  ... 
doi:10.1007/978-3-642-02384-2_6 fatcat:tdu7qveerjhclpbh3l4i4gmilm

Evading Subspaces Over Large Fields and Explicit List-decodable Rank-metric Codes

Venkatesan Guruswami, Carol Wang, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
We also give explicit subcodes of folded Reed-Solomon (RS) codes with small folding order that are list-decodable (in the Hamming metric) with optimal redundancy, motivated by the fact that list decoding  ...  Our codes are explicit subcodes of the well-known Gabidulin codes, which encode linearized polynomials of low degree via their values at a collection of linearly independent points.  ...  We thank Antonia Wachter-Zeh for bringing to our attention the lack of a Johnson-type bound for list decoding rank-metric codes [24] .  ... 
doi:10.4230/lipics.approx-random.2014.748 dblp:conf/approx/GuruswamiW14 fatcat:3yjuvzbdj5boxfb4pgqkgcokma

Explicit rank-metric codes list-decodable with optimal redundancy [article]

Venkatesan Guruswami, Carol Wang
2013 arXiv   pre-print
We also give explicit subcodes of folded Reed-Solomon (RS) codes with small folding order that are list-decodable (in the Hamming metric) with optimal redundancy, motivated by the fact that list decoding  ...  Our codes are subcodes of the well-known Gabidulin codes, which encode linearized polynomials of low degree via their values at a collection of linearly independent points.  ...  Acknowledgment We thank Antonia Wachter-Zeh for bringing to our attention the lack of a Johnson-type bound for list decoding rank-metric codes [24] .  ... 
arXiv:1311.7084v2 fatcat:ycaqwsudzvdxxgsh52wvrts4fi

Coding with Constraints: Minimum Distance Bounds and Systematic Constructions [article]

Wael Halbawi, Matthew Thill, Babak Hassibi
2015 arXiv   pre-print
Finally, we provide conditions under which each of these bounds can be achieved by choosing our code to be a subcode of a Reed-Solomon code, allowing for efficient decoding.  ...  We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols.  ...  Since all of our constructions are built as subcodes of Reed-Solomon codes, they can be decoded efficiently using standard Reed-Solomon decoders.  ... 
arXiv:1501.07556v2 fatcat:o54rfkbno5gnlaj3ifj4apg5ky

Coding with constraints: Minimum distance bounds and systematic constructions

Wael Halbawi, Matthew Thill, Babak Hassibi
2015 2015 IEEE International Symposium on Information Theory (ISIT)  
Finally, we provide conditions under which each of these bounds can be achieved by choosing our code to be a subcode of a Reed-Solomon code, allowing for efficient decoding.  ...  We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols.  ...  Since all of our constructions are built as subcodes of Reed-Solomon codes, they can be decoded efficiently using standard Reed-Solomon decoders.  ... 
doi:10.1109/isit.2015.7282666 dblp:conf/isit/HalbawiTH15 fatcat:byfm2lmi2zgavjovjf4txujuue

On Error Correction for Physical Unclonable Functions [article]

Sven Puchinger and Sven Müelich and Martin Bossert and Matthias Hiller and Georg Sigl
2015 arXiv   pre-print
We show how better results can be obtained using code classes and decoding principles not used for this scenario before.  ...  These methods are exemplified by specific code constructions which improve existing codes with respect to error probability, decoding complexity and codeword length.  ...  In this paper, we extend our results from [2] and propose code constructions based on generalized concatenated, Reed-Muller and Reed-Solomon codes for the application with PUFs, which have advantages  ... 
arXiv:1501.06698v1 fatcat:67obivsjf5fjpj2eztxne3vck4

Importance of Symbol Equity in Coded Modulation for Power Line Communications [article]

Yeow Meng Chee, Han Mao Kiah, Punarbasu Purkayastha, Chengmin Wang
2013 arXiv   pre-print
In this paper, we extend this coded modulation scheme based on permutation codes to general codes and introduce an additional new parameter that more precisely captures a code's performance against permanent  ...  The use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications system.  ...  ACKNOWLEDGEMENT The authors thank Han Vinck for useful discussions.  ... 
arXiv:1301.2041v2 fatcat:722pissce5g3rf2jfrrpfd5fkm

Explicit Constructions of Two-Dimensional Reed-Solomon Codes in High Insertion and Deletion Noise Regime [article]

Tai Do Duc, Shu Liu, Ivan Tjuawinata, Chaoping Xing
2019 arXiv   pre-print
The first construction gives a family of Reed-Solomon codes with insdel error-correcting capability asymptotic to its length.  ...  The second construction provides a family of Reed Solomon codes with an exact insdel error-correcting capability up to its length.  ...  Safavi-Naini [31] gave constructions of deletion correcting codes by using Reed-Solomon codes and their subcodes.  ... 
arXiv:1909.03426v2 fatcat:54dfgdqqf5fghgehttwfqwt7qe

Importance of Symbol Equity in Coded Modulation for Power Line Communications

Yeow Meng Chee, Han Mao Kiah, Punarbasu Purkayastha, Chengmin Wang
2013 IEEE Transactions on Communications  
In this paper, we extend this coded modulation scheme based on permutation codes to general codes and introduce an additional new parameter that more precisely captures a code's performance against permanent  ...  The use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications system.  ...  Stefano Galli for their constructive and insightful comments, which helped improve the presentation of this work substantially.  ... 
doi:10.1109/tcomm.2013.091213.130025 fatcat:4k2hcgw2prbyljx75awmhvje3y

Importance of symbol equity in coded modulation for power line communications

Yeow Meng Chee, Han Mao Kiah, Punarbasu Purkayastha, Chengmin Wang
2012 2012 IEEE International Symposium on Information Theory Proceedings  
In this paper, we extend this coded modulation scheme based on permutation codes to general codes and introduce an additional new parameter that more precisely captures a code's performance against permanent  ...  The use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications system.  ...  Stefano Galli for their constructive and insightful comments, which helped improve the presentation of this work substantially.  ... 
doi:10.1109/isit.2012.6284285 dblp:conf/isit/CheeKPW12 fatcat:nbd7t4apdvejll4ba5fgljgikq

Some New Results on Equivalency of Collusion-Secure Properties for Reed-Solomon Codes [article]

Myong-Son Sin, Ryul Kim
2013 arXiv   pre-print
It is notable that the concept of subspace subcode of Reed-Solomon code, which was introduced in error-correcting code theory, provides an interesting prospect for our topic.  ...  Theory 49, 2003) proposed a question on the equivalence of identifiable parent property and traceability property for Reed-Solomon code family.  ...  Finally using the concept of subspace subcode introduced in error-correcting code theory, we proposed a new result when the characteristic of finite field is 2.  ... 
arXiv:1311.2346v1 fatcat:e5xoquvhebc35peggafpktslry

Reed-Solomon Subcodes with Nontrivial Traces: Distance Properties and Soft-Decision Decoding [article]

Andrew Thangaraj, Safitha J Raj
2008 arXiv   pre-print
Then we construct certain subcodes of RS codes over GF(2^m) that have a non-trivial binary trace with distances and rates meeting the derived bounds.  ...  Reed-Solomon (RS) codes over GF(2^m) have traditionally been the most popular non-binary codes in almost all practical applications.  ...  SUB REED-SOLOMON CODES In this section, we discuss the construction and basic properties of sub Reed-Solomon (SRS) codes with a nontrivial trace.  ... 
arXiv:0810.0567v1 fatcat:lomjhzllcfhapn5ui7kkbgwjyi

Some new results on equivalency of collusion-secure properties for Reed-Solomon codes

Myong-Son Sin, Ryul Kim
2015 IET Information Security  
It is notable that the concept of subspace subcode of Reed-Solomon code, which was introduced in errorcorrecting code theory, provides an interesting prospect for our topic.  ...  Theory 49, 2003) proposed a question on the equivalence of identifiable parent property and traceability property for Reed-Solomon code family.  ...  Finally using the concept of subspace subcode introduced in error-correcting code theory, we proposed a new result when the characteristic of finite field is 2.  ... 
doi:10.1049/iet-ifs.2014.0551 fatcat:2hohr6e2bzce3bwgoybmiiu6ya

Separation Properties and Related Bounds of Collusion-secure Fingerprinting Codes [article]

Myong-Son Sihn, Ryul Kim
2013 arXiv   pre-print
Next we tried to study some interesting relationship between separation and existence of non-trivial subspace subcodes for Reed-Solomon codes.  ...  In this paper we investigate the separation properties and related bounds of some codes.  ...  Moreira for sending his article [9] by e-mail and offering advices on Silverberg's open problem.  ... 
arXiv:1304.6161v2 fatcat:a6rjutwvr5erbgpv3ycfnr5wbm
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