scholarly journals List decoding of Reed–Solomon codes from a Gröbner basis perspective

2008 ◽  
Vol 43 (9) ◽  
pp. 645-658 ◽  
Author(s):  
Kwankyu Lee ◽  
Michael E. O’Sullivan
Keyword(s):  
Gröbner Basis ◽  
List Decoding ◽  
Grobner Basis ◽  
Reed Solomon Codes

scholarly journals List decoding codes on Garcia–Stictenoth tower using Gröbner basis

2009 ◽  
Vol 44 (12) ◽  
pp. 1657-1661
Author(s):  
M. Prem Laxman Das ◽  
Kripasindhu Sikdar
Keyword(s):  
Gröbner Basis ◽  
List Decoding ◽  
Grobner Basis

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

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