Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An efficient algorithm synthesizing all shortest  q  -linearized-feedback shift-registers generating a given sequence of length  N  over a finite field \BBF qm  is derived and its correctness is proved. This algorithm, which is a generalization of the Berlekamp-Massey algorithm, has time complexity  O ( lN )  O ( N  2 ) operations in \BBF qm , where  l  is the linearized complexity of the sequence. The algorithm can be applied for efficiently solving the key equation when decoding Gabidulin codes.
['Vladimir Sidorenko', 'Gerd Richter', 'Martin Bossert']
I am writing a research paper on a idea Linearized Shift-Register Synthesis
[{"from": "human", "value": "I am writing a research paper on a idea Linearized Shift-Register Synthesis"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An efficient algorithm synthesizing all shortest  q  -linearized-feedback shift-registers generating a given sequence of length  N  over a finite field \\BBF qm  is derived and its correctness is proved. This algorithm, which is a generalization of the Berlekamp-Massey algorithm, has time complexity  O ( lN )  O ( N  2 ) operations in \\BBF qm , where  l  is the linearized complexity of the sequence. The algorithm can be applied for efficiently solving the key equation when decoding Gabidulin codes."}]