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On the decoding of algebraic-geometric codes | IEEE Journals & Magazine | IEEE Xplore

On the decoding of algebraic-geometric codes


Abstract:

A decoding algorithm for algebraic-geometric codes arising from arbitrary algebraic curves is presented. This algorithm corrects any number of errors up to ((d-g-1)/2), w...Show More

Abstract:

A decoding algorithm for algebraic-geometric codes arising from arbitrary algebraic curves is presented. This algorithm corrects any number of errors up to ((d-g-1)/2), where d is the designed distance of the code and g is the genus of the curve. The complexity of decoding equals sigma (n/sup 3/) where n is the length of the code. Also presented is a modification of this algorithm, which in the case of elliptic and hyperelliptic curves is able to correct ((d-1)/2) errors. It is shown that for some codes based on plane curves the modified decoding algorithm corrects approximately d/2-g/4 errors. Asymptotically good q-ary codes with a polynomial construction and a polynomial decoding algorithm (for q>or=361 on some segment their parameters are better than the Gilbert-Varshamov bound) are obtained. A family of asymptotically good binary codes with polynomial construction and polynomial decoding is also obtained, whose parameters are better than the Blokh-Zyablov bound on the whole interval 0< sigma <1/2.<>
Published in: IEEE Transactions on Information Theory ( Volume: 36, Issue: 5, September 1990)
Page(s): 1051 - 1060
Date of Publication: 06 August 2002

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