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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 ...##
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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. ...##
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A Generalised Successive Resultants Algorithm
[chapter]

2016
*
Lecture Notes in Computer Science
*

In this paper, we abstract the core SRA

doi:10.1007/978-3-319-55227-9_9
fatcat:haejcyuy6rfipiyc3bjrj3wole
*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. ...##
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The Function Field Sieve Is Quite Special
[chapter]

2002
*
Lecture Notes in Computer Science
*

With either

doi:10.1007/3-540-45455-1_34
fatcat:46ofpwonlzblxc2b2fuhhkowca
*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 ...##
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Simplified High-Speed High-Distance List Decoding for Alternant Codes
[chapter]

2011
*
Lecture Notes in Computer Science
*

This paper presents a simplified list-decoding

doi:10.1007/978-3-642-25405-5_13
fatcat:tjhbgjyj4zgczf4gakdvwxc3be
*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 ...##
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Efficient Implementation of a CCA2-Secure Variant of McEliece Using Generalized Srivastava Codes
[chapter]

2012
*
Lecture Notes in Computer Science
*

This is

doi:10.1007/978-3-642-30057-8_9
fatcat:7cqur257q5d4hgm7klzw634wyi
*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. ...##
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A Number Theoretic Interpolation Between Quantum and Classical Complexity Classes
[article]

2006
*
arXiv
*
pre-print

This type

arXiv:quant-ph/0604089v2
fatcat:bqi2g2lnfrd6zeao4ziwq5owu4
*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]). ...##
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Efficient Identity Testing and Polynomial Factorization in Nonassociative Free Rings

2017
*
International Symposium on Mathematical Foundations of Computer Science
*

Given

doi:10.4230/lipics.mfcs.2017.38
dblp:conf/mfcs/ArvindDM017
fatcat:ehe7e6qbcrdljbtc6rltwaydaa
*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}. ...##
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Efficient Identity Testing and Polynomial Factorization over Non-associative Free Rings
[article]

2017
*
arXiv
*
pre-print

,x_n}

arXiv:1705.00140v2
fatcat:k7cermilhzawhn6qhcwlvbtwle
*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}. ...##
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Shiftless decomposition and polynomial-time rational summation

2003
*
Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03
*

Together with a summability criterion by Abramov, these are applied

doi:10.1145/860854.860887
dblp:conf/issac/GerhardGSZ03
fatcat:4ue2hslxqfdivob2g3l32fm6pa
*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 . ...##
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Rank Metric Decoder Architectures for Random Linear Network Coding With Error Control

2012
*
IEEE Transactions on Very Large Scale Integration (vlsi) Systems
*

KK codes can also be constructed from Gabidulin codes,

doi:10.1109/tvlsi.2010.2096239
fatcat:rleokmslp5dp5cr4m6q5jfbvlm
*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. ...##
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On Efficient Noncommutative Polynomial Factorization via Higman Linearization
[article]

2022
*
arXiv
*
pre-print

We obtain the following result: Given a noncommutative

arXiv:2202.09883v2
fatcat:bufncnpmcjcr3k3zxxj3zl46zq
*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. ...##
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An Algorithm for Constructing a Smallest Register with Non-Linear Update Generating a Given Binary Sequence
[article]

2013
*
arXiv
*
pre-print

Expected size

arXiv:1306.5596v1
fatcat:n3dxdflem5gyfhu7w2ryi3y2iy
*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 ...##
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Algorithm-based low-power and high-performance multimedia signal processing

1998
*
Proceedings of the IEEE
*

The goal

doi:10.1109/5.687834
fatcat:s7ujyq5ovncsnejzocdcsylqde
*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 . ...##
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Toward an Optimal Quantum Algorithm for Polynomial Factorization over Finite Fields
[article]

2018
*
arXiv
*
pre-print

For polynomials

arXiv:1807.09675v1
fatcat:zecwxx3vx5dcvkshbn55a77eau
*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] . ...
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