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>A type of recurring relation on sequences and efficient decoding of a class of algebraic-geometric codes (Ⅱ)——An efficient decoding algorithm
A type of recurring relation on sequences and efficient decoding of a class of algebraic-geometric codes (Ⅱ)——An efficient decoding algorithm
For a class of algebraic-geometric codes, a type of recurring relation is introduced on the syndrome sequence of an error vector. Then, a new majority yoting scheme is developed. By applying the generalized Berlekamp-Massey algorithm, and incorporating the majority voting scheme, an efficient decoding algorithm up to half the Feng-Rao bound is developed for a class of algebraic-geometric codes, the complexity of which is O （ γo1n2）, where n is the code length, and γ is the genus of curve. On different algebraic curves, the complexity of the algorithm can be lowered by choosing base functions suitably. For example, on Hermitian curves the complexity is O(n7/3.
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