m-continued Fraction Expansions of Multi-Laurent Series

m-continued Fraction Expansions of Multi-Laurent Series

戴宗铎,王鲲鹏,叶顶峰

DAI Zong-duo WANG Kun-peng YE Ding-feng

State Key Laboratory of Information Security, Graduate School of Chinese Academy of Science, Beijing, 100039, P. R. China,State Key Laboratory of Information Security, Graduate School of Chinese Academy of Science, Beijing, 100039, P. R. China,State Key L

(State Key Laboratory of Information Security, Graduate School of Chinese Academy of Science, Beijing, 100039, P. R. China

摘要 The simple continued fraction expansion of a single real number gives the best solution to its rational approximation problem. A multidimensional generalization of the simple continued fraction expanding procedure is the Jacobi-Perron algorithm (JPA). This algorithm and its modifications are borrowed to study the multi-rational approximation problem over the formal Laurent series field F((z~(-1))), which is related to the multi-sequence synthesis problem in the field of communication and cryptography, but none of these algorithms guanrantee the best