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.
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Wang, LP. (2006). The Vector Key Equation and Multisequence Shift Register Synthesis. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2006. Lecture Notes in Computer Science, vol 3857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617983_6
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DOI: https://doi.org/10.1007/11617983_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31423-3
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