Details:
Title  Fast computation of Gr\"obner basis of homogeneous ideals of $mathbbF[x, y]$.  Author(s)  PeiZhong Lu, Yan Zou  Type  Article in Journal  Abstract  This paper provides a fast algorithm for Gröbner bases of homogenous ideals of 𝔽[x, y] over a finite field 𝔽. We show that only the Spolynomials of neighbor pairs of a strictly ordered finite homogenours generating set are needed in the computing of a Gröbner base of the homogenous ideal. It reduces dramatically the number of unnecessary Spolynomials that are processed. We also show that the computational complexity of our new algorithm is O(N 2), where N is the maximum degree of the input generating polynomials. The new algorithm can be used to solve a problem of blind recognition of convolutional codes. This problem is a new generalization of the important problem of synthesis of a linear recurring sequence.  Keywords  homogenous ideal, Gröbner basis, sequence synthesis  ISSN  10092757 
URL 
http://link.springer.com/article/10.1007%2Fs1143200800322 
Language  English  Journal  Sci. China, Ser. F  Volume  51  Number  4  Pages  368380  Publisher  Springer, Heidelberg; Science in China Press, Beijing  Year  2008  Edition  0  Translation 
No  Refereed 
No 
