论文标题
解码的芦苇 - 溶剂偏差差异代码
Decoding Reed-Solomon Skew-Differential Codes
论文作者
论文摘要
构建了一大批MD线性代码。这些代码具有有效的解码算法。代码的定义及其解码算法的设计都只需要线性代数方法，这使其每个人都可以完全加以加以加以实现。因此，本文的第一部分通过奇偶校验检查矩阵形成了代码的直接表示，而解码算法则基于矩阵和线性地图操纵。将解码算法正确性的证明所需的更复杂的数学上下文（非共同环）推迟到第二部分。最后一节定位了此处介绍的Reed-Solomon偏差分化代码，该代码在通过偏斜多项式环定义的代码的一般上下文中。
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making them fully accesible for everyone. Thus, the first part of the paper develops a direct presentation of the codes by means of parity-check matrices, and the decoding algorithm rests upon matrix and linear maps manipulations. The somewhat more sophisticated mathematical context (non-commutative rings) needed for the proof of the correctness of the decoding algorithm is postponed to the second part. A final section locates the Reed-Solomon skew-differential codes introduced here within the general context of codes defined by means of skew polynomial rings.
