Abstract
In this paper, we review various decoding methods of algebraic geometry (or algebraic-geometric) codes (Goppa in Soviet Math. Dokl. 24(1):170–172, 1981; Hoholdt et al. in Handbook of coding theory, vols. I, II, North-Holland, Amsterdam, pp. 871–961, 1998; Geil in Algebraic geometry codes from order domains, this volume, pp. 121–141, 2009) mainly based on the Grobner basis theory (Buchberger in Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, Ph.D. thesis, Innsbruck, 1965; Aequationes Math. 4:374–383, 1970; Multidimensional systems theory, Reidel, Dordrecht, pp. 184–232, 1985; London Math. Soc. LNS 251:535–545, 1998; J. Symb. Comput. 41(3–4):475–511, 2006; Mora in Grobner technology, this volume, pp. 11–25, 2009b) as well as the BMS algorithm (Sakata in J. Symbolic Comput. 5(3):321–337, 1988; Inform. and Comput. 84(2):207–239, 1990) and its variations (Sakata in n-dimensional Berlekamp–Massey algorithm for multiple arrays and construction of multivariate polynomials with preassigned zeros, LNCS, vol. 357, pp. 356–376, 1989; Finding a minimal polynomial vector set of a vector of nD arrays, LNCS, vol. 539, pp. 414–425, 1991), where the BMS algorithm itself is reviewed in another paper (Sakata in The BMS algorithm, this volume, pp. 143–163, 2009) in this issue. The main subjects are:
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
