关于两个连续整数生成的半群和改进的Hermitian码
On Semigroups Generated by Two Consecutive Integers and Improved Hermitian Codes
摘要：
通过对一点码的Berlekamp-Massey-Sakata译码算法的分析，提出了两种提高码速率的方法。Feng和Rao提出的一种方法是删除奇偶检验，而这些校验可以通过他们的多数表决算法恢复。第二种方法是将代码设计为仅校正给定权重的几何通用的那些误差向量。在这项工作中，公式给出的厄米特码的冗余优化这些标准以及公式的顺序上的最小距离的限制。结果从分析两个连续整数生成的数值半群。最优厄米特码的冗余度公式纠正了给定数量的错误，回答了Pellikaan和Torres在1999年提出的一个开放性问题。
英文摘要：
Analysis of the Berlekamp-Massey-Sakata algorithm for decoding one-point codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm. The second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic. In this work, formulae are given for the redundancies of Hermitian codes optimized with respect to these criteria as well as the formula for the order bound on the minimum distance. The results proceed from an analysis of numerical semigroups generated by two consecutive integers. The formula for the redundancy of optimal Hermitian codes correcting a given number of errors answers an open question stated by Pellikaan and Torres in 1999.
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