ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 01 Dec 2021 21:26:33 GMT2021-12-01T21:26:33Z5021- The vector key equation and multisequence shift register synthesishttps://scholarbank.nus.edu.sg/handle/10635/130613Title: The vector key equation and multisequence shift register synthesis
Authors: Wang, L.-P.
Abstract: We introduce the vector key equation for cyclic codes with more than one set of consecutive roots. Using the lattice basis reduction multisequence shift register synthesis algorithm [7,8], we find the minimal solution to the vector equation key and also give an important parameter of the multiple sequences, that is, characteristic sequence. Using it, we give a simpler sufficient and necessary condition for the uniqueness of the minimal polynomial of multiple sequences than that in [7]. The new approach enables us not only to decode cyclic codes up to HT and Roos bounds and but also to find out certain error patterns which can be decoded beyond the two bounds. © Springer-Verlag Berlin Heidelberg 2006.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1306132006-01-01T00:00:00Z
- On the lattice basis reduction multisequence synthesis algorithmhttps://scholarbank.nus.edu.sg/handle/10635/129957Title: On the lattice basis reduction multisequence synthesis algorithm
Authors: Wang, L.-P.; Zhu, Y.-F.; Pei, D.-Y.
Abstract: A lattice basis reduction multisequence synthesis (LBRMS) algorithm was presented with a new, intuitive and vector-form model. In this correspondence, a retined version of the LBRMS algorithm is deduced, from which Massey's conjectured algorithm can be derived. Moreover, if we modify the lattice basis reduction algorithm used in the LBRMS algorithm, a new synthesis algorithm is deduced, which is equivalent to the generalization of the Berlekamp-Massey algorithm proposed by Feng and Tzeng. Therefore, the LBRMS algorithm provides a unified approach to the multisequence shift-register synthesis problem. © 2004 IEEE.
Mon, 01 Nov 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1299572004-11-01T00:00:00Z