Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This correspondence contains a straightforward generalization of decoding of BCH codes to the decoding of algebraic-geometric codes, couched in terms of varieties, ideals, and Grobner bases. This consists of 1) a Berlekamp-Massey-type lattice-shifting row-reduction algorithm with majority voting similar to algorithms in the current literature, 2) a realization that it produces a minimal Grobner basis B for the error-locator ideal I(V) relative to a particular ighted total degree monomial ordering, 3) a factoring of that basis into several minimal PLEX bases, that facilitates finding the variety V of error positions, and 4) a direct generalization of Forney's formula to calculate error magnitudes using functions /spl sigma/p, which are by-products of this factoring.
['Douglas A. Leonard']
I am writing a research paper on a idea A generalized Forney formula for algebraic-geometric codes
[{"from": "human", "value": "I am writing a research paper on a idea A generalized Forney formula for algebraic-geometric codes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This correspondence contains a straightforward generalization of decoding of BCH codes to the decoding of algebraic-geometric codes, couched in terms of varieties, ideals, and Grobner bases. This consists of 1) a Berlekamp-Massey-type lattice-shifting row-reduction algorithm with majority voting similar to algorithms in the current literature, 2) a realization that it produces a minimal Grobner basis B for the error-locator ideal I(V) relative to a particular ighted total degree monomial ordering, 3) a factoring of that basis into several minimal PLEX bases, that facilitates finding the variety V of error positions, and 4) a direct generalization of Forney's formula to calculate error magnitudes using functions /spl sigma/p, which are by-products of this factoring."}]