scholarly journals Sharp precision in Hensel lifting for bivariate polynomial factorization

2006 ◽  
Vol 75 (254) ◽  
pp. 921-934 ◽  
Author(s):  
Grégoire Lecerf
Keyword(s):  
Polynomial Factorization ◽  
Bivariate Polynomial ◽  
Hensel Lifting

scholarly journals An application of bivariate polynomial factorization on decoding of Reed-Solomon based codes

2018 ◽  
Vol 12 (1) ◽  
pp. 166-177
Author(s):  
Ivan Pavkov ◽  
Nebojsa Ralevic ◽  
Ljubo Nedovic
Keyword(s):  
Efficient Algorithm ◽  
Sufficient Condition ◽  
Polynomial Factorization ◽  
Necessary And Sufficient Condition ◽  
Bivariate Polynomials ◽  
Bivariate Polynomial ◽  
Integer Coefficients ◽  
Necessary And Sufficient ◽  
The Given

A necessary and sufficient condition for the existence of a non-trivial factorization of an arbitrary bivariate polynomial with integer coefficients was presented in [2]. In this paper we develop an efficient algorithm for factoring bivariate polynomials with integer coefficients. Also, we shall give a proof of the optimality of the algorithm. For a given codeword, formed by mixing up two codewords, the algorithm recovers those codewords directly by factoring corresponding bivariate polynomial. Our algorithm determines uniquely the given polynomials which are used in forming the mixture of two codewords.

Exact bivariate polynomial factorization over ℚ by approximation of roots

2014 ◽  
Vol 28 (1) ◽  
pp. 243-260 ◽  
Author(s):  
Yong Feng ◽  
Wenyuan Wu ◽  
Jingzhong Zhang ◽  
Jingwei Chen
Keyword(s):  
Polynomial Factorization ◽  
Bivariate Polynomial

Sparse bivariate polynomial factorization

2014 ◽  
Vol 57 (10) ◽  
pp. 2123-2142 ◽  
Author(s):  
WenYuan Wu ◽  
JingWei Chen ◽  
Yong Feng
Keyword(s):  
Polynomial Factorization ◽  
Bivariate Polynomial
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