Shojiro Sakata

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We present an algorithm for finding a minimal set of two-dimensional linear recurring relations capable of generating a prescribed finite two-dimensional array. This is a twodimensional extension of the Berlekamp-Massey algorithm for synthesizing a shortest linear feedback shift-register capable of generating a given finite sequence. The complexity of(More)
E FFICIENT decoding of BCHand Reed-Solomon codes can be done by using the Berlekamp-Massey algorithm [ 11, and it is natural to try to use the extension to N dimensions of Sakata [2] to decode algebraic-geometric codes. For codes from regular plane curves this was done in [3] and using the Feng-Rao majority scheme from [4], the procedure was extended in [S](More)
We present a decoding algorithm for algebraicgeometric codes from regular plane curves, in particular the Hermitian curve, which corrects all error patternes of weight less than d*/2 with low complexity. The algorithm is based on the majority scheme of Feng and Rao and uses a modified version of Sakata’s generalization of the Berlekamp-Massey algorithm.
Since before we have proposed a systolic array architecture for implementing fast decoding algorithm of one point AG codes. In this paper we propose a revised architecture which is as its main framework a one-dimensional systolic array, in details, composed of a threedimensional arrangement of processing units called cells, and present a method of complete(More)
Multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions, which have multiple poles and/or zeros on an algebraic curve. Thus, they are more general than one-point codes, which are an important class of algebraic geometry codes in the sense that they can be decoded efficiently using the Berlekamp-Massey-Sakata(More)