Design and Construction of Algebraic-Geometry Codes

提出了基于广义最小距离译码的快速译码算法。这是通过完成Kotter的解码算法得到的。我们引入了一个辅助多项式，通过它建立了完美的迭代解码过程。可以轻松设计硬件实现。新的解码过程可以被认为是 Welch-Berlekamp 方法的反向类型。在Welch-Berlekamp方法中，总是需要耗时的综合症计算，而我们的方法从简单的硬决策解码开始。通过推广我们的方法，代数几何码也可以快速解码。此外，开发了一种能够超越 BCH 界限的新解码程序，其需要的计算时间少于传统情况（即 Blahut 和 Horiguchi 方法）的 1/6 倍。

Fast decoding algorithm is proposed, base on the Generalized Mimimum Distant decoding. This is obtained by completing Kotter's decoding algorithm. We introduce an auxiliary polynomial by which a perfect iterative decoding procedure is established. Hardware inplementations can be easily designed. The new decoding procedure can be thought as a reverse direction type of Welch-Berlekamp method. In the Welch-Berlekamp method, a time-consuming syndrome calculation is always required, whereas our wethod begins with a simple hard-decision decoding. Algebraic-Geometry codes can be also fastly decoded by generalizing our method.Furthermore, a new decoding procedure capable to the beyond BCH bound, is developed which needs a short computation time less then 1/6 times a conventional case, i.e., Blahut and Horiguchi method.