Fast Computations of Gröbner Bases and Blind Recognitions of Convolutional Codes

Authors:
Peizhong Lu;Yan Zou
Affiliations:
Fudan University, Shanghai 200433, P.R. China;Fudan University, Shanghai 200433, P.R. China
Venue:
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Year:
2007

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Abstract

This paper provides a fast algorithm for Gröbner bases of homogenous ideals of the ring $\Bbb{F}[x,y]$ over a field $\Bbb{F}$. The computational complexity of the algorithm is O(N2), where Nis 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 is a new generalization of the important problem of synthesis of a linear recurring sequence.