id: 01365186
dt: j
an: 01365186
au: Leonard, Douglas A.
ti: Efficient Forney functions for decoding AG codes.
so: IEEE Trans. Inf. Theory 45, No.1, 260-265 (1999).
py: 1999
pu: Institute of Electrical and Electronics Engineers (IEEE), New York, NY
la: EN
cc: 
ut: algebraic geometric codes; Forney formula; FGLM algorithm
ci: Zbl 0864.94036
li: doi:10.1109/18.746805
ab: Summary: Using a Forney formula to solve for the error magnitudes in
    decoding AG codes requires producing functions $σ_P$, which are $0$ at
    all but one point $P$ of the variety of the error-locator ideal. The
    best such function is produced here in a reasonably efficient way from
    a {\it lex} Gröbner basis. This {\it lex} basis is, in turn, produced
    efficiently from a weighted, {\it grevlex} basis by using the FGLM
    algorithm. These two steps essentially complete the efficient decoding
    scheme based on a Forney formula started in the author’s previous
    work [ibid. 42, 1263-1268 (1996; Zbl 0864.94036)].
rv: