Evaluation codes from order domain theory
Evaluation codes from order domain theory
复制标题
来自阶域理论的评估代码
DOI：
10.1016/j.ffa.2006.12.004
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Olav Geil
中科院分区：
文献类型：
--
作者：
Henning E. Andersen;Olav Geil
著名的冯-饶界估计了由码的奇偶校验矩阵定义的码的最小距离。从冯-饶界可以清楚地看出，如何通过省略奇偶校验矩阵中的某些行来改进一大类码。本文利用码的生成矩阵给出了码的最小距离的一个简单下界。根据我们的界限，很清楚如何通过向其生成矩阵添加某些行来改进一大类代码。新的界与冯-饶界以及Shibuya和Sakaniwa在[T.Shibuya，K.Sakaniwa，A对偶的良好性能型设计最小距离IEICE Transans中的界有很大关系。基金。E84-A(2001)647-652]。我们的界很容易扩展到处理任何广义Hamming重量。我们将我们的方法解释到有序域理论的背景下。这样，我们填补了序域理论中的一个明显的空白。
The celebrated Feng–Rao bound estimates the minimum distance of codes defined by means of their parity check matrices. From the Feng–Rao bound it is clear how to improve a large family of codes by leaving out certain rows in their parity check matrices. In this paper we derive a simple lower bound on the minimum distance of codes defined by means of their generator matrices. From our bound it is clear how to improve a large family of codes by adding certain rows to their generator matrices. The new bound is very much related to the Feng–Rao bound as well as to Shibuya and Sakaniwa's bound in [T. Shibuya, K. Sakaniwa, A dual of well-behaving type designed minimum distance, IEICE Trans. Fund. E84-A (2001) 647–652]. Our bound is easily extended to deal with any generalized Hamming weights. We interpret our methods into the setting of order domain theory. In this way we fill in an obvious gap in the theory of order domains.