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Synthesis of Finite State Algorithms in a Galois Field GF[p^{n}]
March 1981 (vol. 30 no. 3)
pp. 225229
ASCII Text  x  
W.R. English, "Synthesis of Finite State Algorithms in a Galois Field GF[p<sup>n</sup>]," IEEE Transactions on Computers, vol. 30, no. 3, pp. 225229, March, 1981.  
BibTex  x  
@article{ 10.1109/TC.1981.1675759, author = {W.R. English}, title = {Synthesis of Finite State Algorithms in a Galois Field GF[p<sup>n</sup>]}, journal ={IEEE Transactions on Computers}, volume = {30}, number = {3}, issn = {00189340}, year = {1981}, pages = {225229}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1981.1675759}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Synthesis of Finite State Algorithms in a Galois Field GF[p<sup>n</sup>] IS  3 SN  00189340 SP225 EP229 EPD  225229 A1  W.R. English, PY  1981 KW  sequential networks KW  Finitestate algorithms KW  finitestate machines KW  Galois field arithmetic VL  30 JA  IEEE Transactions on Computers ER   
This correspondence describes a method for achieving synthesis of finite state algorithms by the use of a set of logic elements that execute field operations from the Galois field GF[pn]. The method begins with a definition of the algorithm to be synthesized in a completely specified finite state flow table form. A polynomial expansion of this flow table function is derived. A canonical sequential circuit corresponding to this polynomial expansion is defined. Subsequently, the given algorithm is synthesized using the canonical circuit by specification of a number of arbitrary constants in the canonical circuit. A mechanical method for deriving constants used in the canonical circuits is given. Finally, some estimates on complexity of the given circuit structure are stated assuming the most fundamental logic element structures.
Index Terms:
sequential networks, Finitestate algorithms, finitestate machines, Galois field arithmetic
Citation:
W.R. English, "Synthesis of Finite State Algorithms in a Galois Field GF[p^{n}]," IEEE Transactions on Computers, vol. 30, no. 3, pp. 225229, March 1981, doi:10.1109/TC.1981.1675759
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