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Page 5426 of Mathematical Reviews Vol. , Issue 82m [page]

1982 Mathematical Reviews  
M. 82m:94044 An approach to symbolic analysis of linear electronic circuits. (Russian) Teoret. Elektrotehn. No. 29 (1980), 3-12, 171.  ...  Authors’ summary: “We propose an approach to symbolic analysis of linear electronic circuits that enables us to bracket, in expressions of circuit functions, actually occurring combinations of predetermined  ... 

Page 1118 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews  
Mandelbaum, David M. 87b:94051 An approach to an arithmetic analog of Berlekamp’s algorithm. IEEE Trans. Inform. Theory 30 (1984), no. 5, 758-762.  ...  This paper presents a theoretical approach to a new class of nonbinary arithmetic AN codes using symmetric R-ary expres- sions and Lee-type arithmetic distance.  ... 

A Generalised Successive Resultants Algorithm [chapter]

James H. Davenport, Christophe Petit, Benjamin Pring
2016 Lecture Notes in Computer Science  
In this paper, we abstract the core SRA algorithm to arbitrary finite fields and present three instantiations of our general algorithm, one of which is novel and makes use of a series of isogenies derived  ...  The algorithm was designed to be efficient when the characteristic p is small and n > 1.  ...  The authors would like to thank the anonymous reviewers both for their time and for their helpful advice, much of which was incorporated into the final paper.  ... 
doi:10.1007/978-3-319-55227-9_9 fatcat:haejcyuy6rfipiyc3bjrj3wole

The Function Field Sieve Is Quite Special [chapter]

Antoine Joux, Reynald Lercier
2002 Lecture Notes in Computer Science  
With either of these constructions the FFS becomes an equivalent of the special number field sieve used to factor integers of the form A N ± B.  ...  From an asymptotic point of view, this is faster than older algorithm such as Coppersmith's algorithm and Adleman's original FFS.  ...  Remark: Berlekamp's algorithm has got roughly two phases; the construction of a set of "f-reducing polynomials" thanks to the kernel computation of the Berlekamp's matrix and the separation step itself  ... 
doi:10.1007/3-540-45455-1_34 fatcat:46ofpwonlzblxc2b2fuhhkowca

Simplified High-Speed High-Distance List Decoding for Alternant Codes [chapter]

Daniel J. Bernstein
2011 Lecture Notes in Computer Science  
This paper presents a simplified list-decoding algorithm to correct any number w of errors in any alternant code of any length n with any designed distance t + 1 over any finite field F q ; in particular  ...  The algorithm is efficient for w close to, and in many cases slightly beyond, the F q Johnson bound J = n − n (n − t − 1) where n = n(q − 1)/q, assuming t + 1 ≤ n .  ...  The advantages of this tweaked algorithm over the Koetter-Vardy algorithm are analogous to the advantages of the Howgrave-Graham algorithm over the Guruswami-Sudan algorithm: most importantly, the local  ... 
doi:10.1007/978-3-642-25405-5_13 fatcat:tjhbgjyj4zgczf4gakdvwxc3be

Efficient Implementation of a CCA2-Secure Variant of McEliece Using Generalized Srivastava Codes [chapter]

Pierre-Louis Cayrel, Gerhard Hoffmann, Edoardo Persichetti
2012 Lecture Notes in Computer Science  
This is analogous to RSA using small encryption exponents.  ...  Decryption: Given a ciphertext y, calculate yP −1 = xG P −1 + eP −1 = xSG + eP −1 , and since the weight of eP −1 is still the same, it is enough to apply the decoding algorithm for the code to retrieve  ...  Acknowledgments We would like to thank Steven Galbraith for many fruitful discussions and his constant support throughout the development of the paper.  ... 
doi:10.1007/978-3-642-30057-8_9 fatcat:7cqur257q5d4hgm7klzw634wyi

A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes [article]

J. Maurice Rojas
2006 arXiv   pre-print
This type of quantum/classical interpolation phenomenon appears to new.  ...  a plausible hypothesis involving primes in arithmetic progression (implied by the Generalized Riemann Hypothesis for certain cyclotomic fields), a randomized polynomial time algorithm for (*) would imply  ...  to the dense encoding) are already known (e.g., Berlekamp's algorithm [BS96, Sec. 7 .4]).  ... 
arXiv:quant-ph/0604089v2 fatcat:bqi2g2lnfrd6zeao4ziwq5owu4

Efficient Identity Testing and Polynomial Factorization in Nonassociative Free Rings

Vikraman Arvind, Rajit Datta, Partha Mukhopadhyay, S. Raja, Marc Herbstritt
2017 International Symposium on Mathematical Foundations of Computer Science  
Given an arithmetic circuit C of size s computing a polynomial f ∈ F{x 1 , x 2 , . . . , x n } of degree d, we give an efficient deterministic algorithm to compute circuits for the irreducible factors  ...  Given an arithmetic circuit C of size s computing a polynomial f ∈ F{x 1 , x 2 , . . . , x n } of degree d, we give a deterministic poly(n, s, d) algorithm to decide if f is identically zero polynomial  ...  Consider an arithmetic circuit C computing a polynomial f ∈ F{X}.  ... 
doi:10.4230/lipics.mfcs.2017.38 dblp:conf/mfcs/ArvindDM017 fatcat:ehe7e6qbcrdljbtc6rltwaydaa

Efficient Identity Testing and Polynomial Factorization over Non-associative Free Rings [article]

V. Arvind, Rajit Datta, Partha Mukhopadhyay, S. Raja
2017 arXiv   pre-print
,x_n} of degree d, we give an efficient deterministic algorithm to compute circuits for the irreducible factors of f in time poly(n,s,d) when F=Q.  ...  Our result is obtained by a suitable adaptation of the PIT algorithm of Raz-Shpilka [RS05] for noncommutative ABPs. (2) Given an arithmetic circuit C of size s computing a polynomial f∈F{x_1,x_2,...  ...  Consider an arithmetic circuit C computing a polynomial f ∈ F{X}.  ... 
arXiv:1705.00140v2 fatcat:k7cermilhzawhn6qhcwlvbtwle

Shiftless decomposition and polynomial-time rational summation

J. Gerhard, M. Giesbrecht, A. Storjohann, E. V. Zima
2003 Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03  
Together with a summability criterion by Abramov, these are applied to get a polynomial-time algorithm for indefinite rational summation, using a sparse representation of the output.  ...  New algorithms are presented for computing the dispersion set of two polynomials over É and for shiftless factorization.  ...  In step (4) we factor f and g modulo p (using Berlekamp's algorithm) and lift to a factorization modulo p µ .  ... 
doi:10.1145/860854.860887 dblp:conf/issac/GerhardGSZ03 fatcat:4ue2hslxqfdivob2g3l32fm6pa

Rank Metric Decoder Architectures for Random Linear Network Coding With Error Control

Ning Chen, Zhiyuan Yan, Maximilien Gadouleau, Ying Wang, Bruce W. Suter
2012 IEEE Transactions on Very Large Scale Integration (vlsi) Systems  
KK codes can also be constructed from Gabidulin codes, an important class of rank metric codes.  ...  Due to error propagation, errors greatly deteriorate the throughput of network coding and seriously undermine both reliability and security of data. Hence error control for network coding is vital.  ...  ACKNOWLEDGMENT The authors would like to thank Dr. D. Silva and Prof. F. R. Kschischang for valuable discussions, and thank reviewers for their constructive comments.  ... 
doi:10.1109/tvlsi.2010.2096239 fatcat:rleokmslp5dp5cr4m6q5jfbvlm

On Efficient Noncommutative Polynomial Factorization via Higman Linearization [article]

V. Arvind, Pushkar S. Joglekar
2022 arXiv   pre-print
We obtain the following result: Given a noncommutative arithmetic formula of size s computing a noncommutative polynomial f in F as input, where F=F_q is a finite field, we give a randomized algorithm  ...  We use basic elements from Cohn's theory of free ideals rings combined with Ronyai's randomized polynomial-time algorithm for computing invariant subspaces of a collection of matrices over finite fields  ...  Hence, our approach to noncommutative polynomial factorization does not yield an efficient algorithm over Q. Suppose f ∈ F X is given by a noncommutative arithmetic formula.  ... 
arXiv:2202.09883v2 fatcat:bufncnpmcjcr3k3zxxj3zl46zq

An Algorithm for Constructing a Smallest Register with Non-Linear Update Generating a Given Binary Sequence [article]

Nan Li, Elena Dubrova
2013 arXiv   pre-print
Expected size of RNLUs constructed by the presented algorithm is proved to be O(n/log(n/p)), where n is the sequence length and p is the degree of parallelization.  ...  This is asymptotically smaller than the expected size of RNLUs constructed by previous algorithms and the expected size of LFSRs and NLFSRs generating the same sequence.  ...  There were many subsequent extensions and improvements of the algorithm, for example Mandelbaum [28] developed its arithmetic analog, Imamura and Yoshida [29] presented an alternate and easier derivation  ... 
arXiv:1306.5596v1 fatcat:n3dxdflem5gyfhu7w2ryi3y2iy

Algorithm-based low-power and high-performance multimedia signal processing

K.J. Ray Liu, An-Yeu Wu, A. Raghupathy, Jie Chen
1998 Proceedings of the IEEE  
The goal of this paper is to demonstrate the flexibility and effectiveness of algorithmbased approaches and to show that the multirate approach is an effective and systematic design methodology to achieve  ...  A digital-signal-processing engine that is an adaptive reconfigurable architecture is also derived from the common features of our approach.  ...  While Peterson's algorithm is inefficient for large , Berlekamp's algorithm and Euclid's algorithm are more efficient for larger .  ... 
doi:10.1109/5.687834 fatcat:s7ujyq5ovncsnejzocdcsylqde

Toward an Optimal Quantum Algorithm for Polynomial Factorization over Finite Fields [article]

Javad Doliskani
2018 arXiv   pre-print
For polynomials of degree n over a finite field _q, the average-case complexity of our algorithm is an expected O(n^1 + o(1)^2 + o(1)q) bit operations.  ...  Only for a negligible subset of polynomials of degree n our algorithm has a higher complexity of O(n^4 / 3 + o(1)^2 + o(1)q) bit operations.  ...  The best known algorithm, as of now, is an implementation of the Kaltofen-Shoup algorithm due to Kedlaya and Umans [14] .  ... 
arXiv:1807.09675v1 fatcat:zecwxx3vx5dcvkshbn55a77eau
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