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Ternary Syndrome Decoding with Large Weight [article]

Rémi Bricout, André Chailloux, Thomas Debris-Alazard, Matthieu Lequesne
2019 arXiv   pre-print
On a more fundamental level, we show that ternary Syndrome Decoding with large weight is a really harder problem than the binary Syndrome Decoding problem, which could have several applications for the  ...  The Syndrome Decoding problem is at the core of many code-based cryptosystems. In this paper, we study ternary Syndrome Decoding in large weight.  ...  Our Contributions Our contribution is to perform a general study of ternary syndrome decoding with large weight. The PGE+SS framework.  ... 
arXiv:1903.07464v2 fatcat:cefqe43yvngjrhobicpbikwjee

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

1986 Mathematical Reviews  
with error probability p, a smaller symbol error probability than decoding using the coset leaders of minimum weight.  ...  In particular, we show that for any syndrome, except the case where m is even and the syndrome terms are s; = 0 and s3 = 1, the corresponding coset is of weight < 3.  ... 

Complete decoding algorithm of (11,6,5) Golay code

S.-W. Wei, G.-H. Wei
1989 Electronics Letters  
links, in the case where differential phase shift is the dominant cause of crosspolarisation, it is proposed to perform adaptive cancellation of the cross-polarisation by means of a simplified network with  ...  5) GOLAY CODE Indexing terms: Codes, Error-correction codes, Decoding, Algorithms A simple complete decoding algorithm for the (11, 6, 5) perfect ternary Golay code is presented.  ...  Furthermore, the syndrome values of a cyclic shift of T(x), Si" and S y ) , can be simply obtained by shifting the syndrome generator of g(x) once with initial contents Si (Reference 5, theorem 8.7).  ... 
doi:10.1049/el:19890798 fatcat:xdrlj4fnfvfsjd7e23uutvzar4

The Golay Codes [chapter]

Mario de Boer, Ruud Pellikaan
1999 Some Tapas of Computer Algebra  
One-step decoding of G 23 In this paragraph we will decode all error patterns of weight 3 that can occur in a codeword of the code G 23 at once by computing the Gröbner basis for variable syndromes S.  ...  The supports of the codewords of weight 8 in G 24 form a 5-design, the unique S(5, 8, 24). 2 Minimal weight codewords of G 11 G 11 is the ternary cyclic code of length 11 with defining set J = {1}.  ... 
doi:10.1007/978-3-662-03891-8_18 fatcat:pu6d2rqrhzdutkx2n5x275jwje

Page 8144 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
Summary: “A new algebraic decoding algorithm for the ternary (11,6,5) Golay code is presented.  ...  (E-BARA-I; Bellaterra (Barcelona)) A new algebraic algorithm to decode the ternary Golay code.  ... 

Modified pqsigRM: RM Code-based Signature Scheme

Yongwoo Lee, Wijik Lee, Young-Sik Kim, Jong-Seon No
2020 IEEE Access  
The proposed decoder samples from coset elements with small Hamming weight for any given syndrome and efficiently finds such an element.  ...  REED-MULLER CODES AND RECURSIVE DECODING  ...  Moreover, finding errors with large Hamming weight for the given syndrome allows small parameters.  ... 
doi:10.1109/access.2020.3026989 fatcat:ozlmqazvojeznh5zh3mwcny2aq

One and Two Bit Message Passing for SC-LDPC Codes with Higher-Order Modulation [article]

Fabian Steiner, Emna Ben Yacoub, Balazs Matuz, Gianluigi Liva, Alexandre Graell i Amat
2019 arXiv   pre-print
efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS).  ...  The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB.  ...  distance decoding (BDD) (e.g., based on the syndrome).  ... 
arXiv:1902.10391v2 fatcat:kv75xyks25bnxaaqw5d3nn2wpe

A Code-Based Digital Signature Scheme Using Modified Quasi-Cyclic Low-Density Parity-Check Codes (QC-LDPC)

2019 International Journal of Engineering and Advanced Technology  
The major drawback of this algorithm is its large publickey size.  ...  Due to this problem of CFS algorithm, new scheme is presented in this paper using the modified Quasi Cyclic LDPC code and LLR-BP decoding algorithm by replacing the Goppa code and the Patternson decoding  ...  The hash function 'h' of the proposed algorithm depends on the syndrome decoding problem i.e. SD problem.  ... 
doi:10.35940/ijeat.f8822.088619 fatcat:4ban6rpicjcvfpyclewahcjs3a

At the Dawn of the Theory of Codes

Alexander Barg
1993 The Mathematical intelligencer  
Recently, the BMA was generalized to 2-and N-dimensional syndrome arrays [22] and applied to the decoding of algebraic-geometric codes.  ...  A natural question is: How large can the distance of a code of length n with M words be? or, how many words can there be in a code of length n and with distance d?  ... 
doi:10.1007/bf03025254 fatcat:kqoqgrxuxvemdjrbswawuttv4i

On the existence of PD-sets: Algorithms arising from automorphism groups of codes

Nicola Pace, ,Chair of Operations Research - Technische Universität München, Arcisstr. 21, 80333 Munich, Germany, Angelo Sonnino, ,Dipartimento di Matematica, Informatica ed Economia - Università degli Studi della Basilicata, Viale dell'Ateneo Lucano, 10, 85100 Potenza, Italy
2019 Advances in Mathematics of Communications  
In general, the algorithm works well whenever the code C has a very large automorphism group. 2010 Mathematics Subject Classification: Primary: 94B05, 94B35; Secondary: 20B25.  ...  A computational approach is proposed and illustrated with two exceptional codes with automorphism groups isomorphic to the sporadic simple groups M 12 and M 22 , respectively.  ...  If r = c + e is a vector with c ∈ C and w(e) ≤ t, then the information symbols in r are correct if and only if the weight of the syndrome T s = H · T r of r does not exceed t.  ... 
doi:10.3934/amc.2020065 fatcat:mxhxz5vzrfaqhbdmz7x2vnds4m

Signature codes for weighted noisy adder channel, multimedia fingerprinting and compressed sensing

Elena Egorova, Marcel Fernandez, Grigory Kabatiansky, Moon Ho Lee
2018 Designs, Codes and Cryptography  
Our approach is based on the theory of the signature codes for multiple access channels, mainly, for a weighted noisy adder channel.  ...  Hence, each coalition J with chosen weights λ j corresponds to the following uniquely defined ternary output vector D(S(J )), which we call discrete signature of J , where D is the following mapping of  ...  We show that the signature codes for such channel is the same as the multimedia fingerprinting codes with soft decoding.  ... 
doi:10.1007/s10623-018-0580-4 fatcat:36o4ehxebvcthpdsmbmaobcgxy

Page 5064 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
The algorithm consists of Gaussian elimination on a specially arranged syndrome matrix, followed by a novel majority voting scheme.  ...  Second, the code construction with its decoding algorithm can be formulated over the integer ring, providing an algebraic approach to correcting errors in partial-response channels where matched spectral-null  ... 

Decoding square-free Goppa codes over _p [article]

Paulo S. L. M. Barreto and Rafael Misoczki and Richard Lindner
2012 arXiv   pre-print
If the code in question has degree t and the average distance to the closest codeword is at least (4/p)t + 1, the proposed decoder can uniquely correct up to (2/p)t errors with high probability.  ...  We propose a new, efficient non-deterministic decoding algorithm for square-free Goppa codes over _p for any prime p.  ...  The syndrome decoding problem consists of computing the error pattern e given its syndrome s e .  ... 
arXiv:1103.3296v2 fatcat:ej2dspquj5dbvcr2hprtg7j77i

A Soft-Aided Staircase Decoder Using Three-Level Channel Reliabilities [article]

Yi Lei, Bin Chen, Gabriele Liga, Alexios Balatsoukas-Stimming, Kaixuan Sun, Alex Alvarado
2021 arXiv   pre-print
Additional gains of up to 0.53 dB with respect to SABM and 0.91 dB with respect to standard SCC decoding at a bit error rate of 10^-6 are reported.  ...  The decoding complexity of iSABM is comparable of that of SABM.  ...  decoders are typically used for example to decode low density parity check codes (LDPC) and provide large coding gains.  ... 
arXiv:2103.09991v1 fatcat:bb5zch7pjfba3jma4nyzkghwva

Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces

B. K. Dass, Namita Sharma, Rashmi Verma
2018 Advances in Mathematics of Communications  
All poset block structures turning the extended binary and ternary Golay codes into 1-perfect codes are classified. 2010 Mathematics Subject Classification: Primary: 94B05; Secondary: 94B60.  ...  In [6] , Felix and Firer have established that syndrome decoding for hierarchical poset codes offers an exponential gain in comparison to the usual syndrome decoding of linear codes and, further, reduces  ...  The error-correction capability of a code is largely determined by its minimum distance.  ... 
doi:10.3934/amc.2018037 fatcat:6thmiawbfnajjnmayogyyvxvee
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