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Page 3042 of Mathematical Reviews Vol. , Issue 94e
[page]

1994
*
Mathematical Reviews
*

94e:94010
94e:94010 94A55 68Q40 Sakata, Shojiro

*Finding**a**minimal**polynomial**vector**set**of**a**vector**of**nD**arrays*. ...*arrays**of*the given*vector*while the latter*finds**a**minimal**set**of*linear recurrences which are in common to all the given*nD**arrays*.” ...##
###
Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm

1994
*
Mathematics of Computation
*

Once one has the

doi:10.2307/2153413
fatcat:gbnf77u65fckxmbs6qwzcjivqu
*minimal**polynomial*f*of*B , one can*set*f-(3,) = f(3,)/Ak (dividing by the highest possible power*of**A*) , compute f -( B ) z for any*vector*z , and apply powers*of*B successively until ... < 1 + 1 For any univariate*polynomial*r ( 1 ) over G F ( 2 ) , define and*set*dm= min, dm(i). Clearly, any*polynomial*r achieving this minimum is*a*divisor*of*f , the*minimal**polynomial**of*B . ...##
###
Solving homogeneous linear equations over ${\rm GF}(2)$ via block Wiedemann algorithm

1994
*
Mathematics of Computation
*

*A*block version

*of*the algorithm allows us to perform 32 matrix-

*vector*operations for the cost

*of*one. ... We propose

*a*method

*of*solving large sparse systems

*of*homogeneous linear equations over GF(2), the field with two elements. We modify an algorithm due to Wiedemann. ... In particular, Odlyzko suggested that the Wiedemann algorithm might be converted to block form, after we had discussed the present author's similar work on

*a*...

##
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Extension of the Berlekamp-Massey algorithm to N dimensions

1990
*
Information and Computation
*

By it we can

doi:10.1016/0890-5401(90)90039-k
fatcat:gtwevola2vblbmnwjmcrnuhdji
*find**a**minimal**set**of*linear recurring (LR) relations which are valid for*a*given two-dimensional (2D)*array*over any finite field. ... We present an algorithm for*finding**a**minimal**set**of*linear recurring relations which are valid for*a*given n-dimensional*array*over any field, where the "*minimality*" is defined with respect to the partial ...*of*any*minimal**polynomial**set*having order between q and p must have degree equal to some s E S. ...##
###
Computing in GF(q)

1974
*
Mathematics of Computation
*

The third type

doi:10.2307/2005374
fatcat:er7d4auo5rgitdky5wp7pqnxxq
*of*primitive*polynomial*examined permits the given representation*of*GF(<jr) to display*a*primitive normal basis over GF(p). ... This paper gives an elementary deterministic algorithm for completely factoring any*polynomial*over GF(q), q = p , criteria for the identification*of*three types*of*primitive*polynomials*, an exponential ... The*set**of*all scalar matrices aln*of*order n,*a*€ F, is and that g{x) is the*minimal**polynomial**of*C(g{x)) over F. ...##
###
Sparse FGLM algorithms

2017
*
Journal of symbolic computation
*

,xn]

doi:10.1016/j.jsc.2016.07.025
fatcat:ru42mttthveglibwl3wxpsoqx4
*of*degree D, the transformation*of*the ordering*of*its Groebner basis from DRL to LEX is*a*key step in*polynomial*system solving and turns out to be the bottleneck*of*the whole solving process. ... Furthermore, for generic*polynomial*systems, we present an explicit formula for the estimation*of*the sparsity*of*one main multiplication matrix, and prove its construction is free. ... This work is supported by the EXACTA grant*of*the French National Research Agency (ANR-09-BLAN-0371-01) and the National Science Foundation*of*China (NSFC 60911130369), the HPAC grant*of*the French National ...##
###
Fast algorithm for change of ordering of zero-dimensional Gröbner bases with sparse multiplication matrices

2011
*
Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11
*

This almost matches the complexity

doi:10.1145/1993886.1993908
dblp:conf/issac/FaugereM11
fatcat:sboyn2mw7zgc7jqiiyflj5a254
*of*computing the*minimal**polynomial**of*one multiplication matrix. Then, we address the general case and give corresponding complexity results. ... ,x n ] be*a*0-dimensional ideal*of*degree D where K is*a*field. ... BMS The BMS algorithm is one that can be used to*find*the*minimal**set*w.r.t.*a*term ordering <*of**a*linearly recurring relation generated by*a*given multi-dimensional*array*[18, 19, 17] . ...##
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Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound

1995
*
IEEE Transactions on Information Theory
*

The Sakata algorithm is

doi:10.1109/18.476248
fatcat:c3n4hb6w6jby3jrhiiddwbzrwm
*a*generalization to N dimensions*of*the classical Berlekamp-Massey algorithm. ... Abstiuct-We treat*a*general class*of*algebraic-geometric codes and show how to decode these up to half the Feng-Rao bound, using an extension and modification*of*the Sakata algorithm. ... The complexity*of**finding**a*reduced*minimal**polynomial**set*for the*array**of*known syndromes is O(al(m -g + 1)2). 3) To calculate the candidate values for SZ where O(7) = m + 1 costs at most al (m -g) operations ...##
###
Efficiency improvement in an nD systems approach to polynomial optimization

2007
*
Journal of symbolic computation
*

The problem

doi:10.1016/j.jsc.2006.03.008
fatcat:yvog4tjwujhdnlx2eff2b6qzle
*of**finding*the global minimum*of**a*so-called Minkowski-norm dominated*polynomial*can be approached by the matrix method*of*Stetter and Möller, which reformulates it as*a*large eigenvalue problem ... This paper focuses on improving the efficiency*of*computing the action*of*the matrix on*a**vector*. ... In this paper we present*a*technique which uses*nD*systems for*finding*the global minimum*of**a*special class*of*dominated*polynomials*. ...##
###
A Polycyclic Quotient Algorithm

1998
*
Journal of symbolic computation
*

*A*practical algorithm is one which will work well on average, even though in the worst case, the run time may not be

*polynomial*. ... The algorithm involves

*a*generalization

*of*the Gr obner basis method

*of*commutative ring theory to the integral group ring

*of*

*a*polycyclic group. ... We will start by nding

*a*

*set*P 0 which we will prove is

*a*

*minimal*Gr obner basis. Let M P be the

*set*

*of*all leading monomial

*vectors*

*of*the

*polynomial*

*arrays*in P. ...

##
###
An approach to checking link conflicts in the mapping of uniform dependence algorithms into lower dimensional processor arrays

1999
*
IEEE transactions on computers
*

*arrays*. ... In order to enumerate integer solutions efficiently,

*a*representation

*of*the integer solutions is devised so that the size

*of*the space enumerated is yPx nÀk . ... ACKNOWLEDGMENTS This research was supported by the National Science Council

*of*the Republic

*of*China under contract NSC88-2213-E-036-003. ...

##
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Protection of Information from Imitation on the Basis of Crypt-Code Structures
[article]

2018
*
arXiv
*
pre-print

*A*system is offered for imitation resistant transmitting

*of*encrypted information in wireless communication networks on the basis

*of*redundant residue

*polynomial*codes. ... The use

*of*authentication codes as

*a*means

*of*one

*of*the levels to detect erroneous blocks in the ciphertext in combination with the redundant residue

*polynomial*codes

*of*deductions makes it possible to ... the

*vector*

*of*redundant encrypted symbols {ϑ k+1 (z), ϑ k+2 (z), . . . , ϑ n (z)} ∈ B, where

*A*is the

*array*

*of*blocks

*of*the ciphertext, B is

*a*finite

*array*. ...

##
###
A Class of Factorial Designs with Unequal Cell-Frequencies

1960
*
The Annals of Mathematical Statistics
*

The fact that permitted us to look for an inverse

doi:10.1214/aoms/1177705801
fatcat:qcznkgptbzabdihc3cu5x5fasu
*of**a*linear*polynomial*in CLASS*OF*FACTORIAL DESIGNS 755 Ay among the*set**of*linear*polynomials*in*A*,, is the degree*of**minimal*poly- nomial*of**A*,, : it ... In general, the inverse*of*any regular matrix P that is*a**polynomial*P(*A*), where*A*has*a**minimal**polynomial**of*degree r, can be written as Q(*A*), Q being*of*degree r — 1 at most. ...##
###
An Adaptive CM Array Preconditioner for Blind Multi-User Separation
[article]

2018
*
arXiv
*
pre-print

With rigorous theoretical analysis

arXiv:1807.09692v1
fatcat:rqhq65ae4zaxdpefgtrp3j6ys4
*of*the*array*response based on the discrete-space Fourier transform we elaborate*a*solution that solves the problem by*finding*the roots*of**a**polynomial*equation. ... Based on the observation that the differential filter weights resemble*a*superposition*of*the*array*steering*vectors*, we cast the original task to*a*direction-*of*-arrival estimation problem. ... ACKNOWLEDGMENT The authors would like to thank the Brazilian research and innovation agencies FAPDF (Fundação de Apoio*à*Pesquisa do Distrito Federal), CAPES (Coordenação de Aperfeiçoamento de Pessoal ...##
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Backtracking Search Optimization Paradigm for Pattern Correction of Faulty Antenna Array in Wireless Mobile Communications

2019
*
Wireless Communications and Mobile Computing
*

*A*fitness function is developed to optimize the weights

*of*the remaining healthy antenna elements in the

*array*. ... Every antenna

*array*is projected to generate

*a*desired pattern and, hence, failure

*of*any antenna causes misrepresentation

*of*the overall pattern in terms

*of*increased side lobe levels and displacement ... [31] in which

*a*steering

*vector*based null positioning is proposed. ...

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