A Fast Decoding Method of AG Codes from Miura-Kamiya Curves Cab up to Half the Feng-Rao Bound
✍ Scribed by S. Sakata; J. Justesen; Y. Madelung; H.E. Jensen; T. Høholdt
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 796 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1071-5797
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✦ Synopsis
We present a fast version of the Feng-Rao algorithm for decoding of one-point algebraic-geometric (AG) codes derived from the curves which Miura and (\mathrm{Ka}-) miya classified as (C_{a b}). Our algorithm performs the Feng-Rao algorithm efficiently by using the Sakata algorithm, i.e., the 2D Berlekamp-Massey algorithm. One can decode the one-point (\mathrm{AG}) codes up to half of the Feng-Rao bound (d_{\mathrm{FR}}) which is greater than or equal to the designed distance (d^{*}). We have proven the validity and the performance of our algorithm in the framework of our own theory, depending little on algebraic geometry. 1995 Academic Press, Inc.