Generalized Hamming weights of trace codes
Generalized Hamming weights of trace codes
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DOI：
10.1109/18.312185
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发表时间：
1994-03
期刊：
影响因子：
--
通讯作者：
H. Stichtenoth;C. Voss
中科院分区：
文献类型：
--
作者：
H. Stichtenoth;C. Voss
F/sub p/上的线性码通常允许将定义在扩张域F/sub p/m上的码的迹码作为自然表示。本文给出了这类迹码的子码权的估计。他们的主要结果是一个深远的推广Carlitz-Uchiyama界的二进制BCH码。特别是，他们证明了一个大类的代码，包括BCH码，经典的Goppa码，Melas码，和任意的长度为n=p/sup m/-1的循环码的广义汉明重量的尖锐的界限。主要工具是理论的代数函数在有限领域，特别是哈塞-韦尔界的地方的次数之一。>
Linear codes over F/sub p/ often admit a natural representation as trace codes of codes that are defined over an extension field F/sub p/m. In the paper, the authors obtain estimates for the weights of subcodes of such trace codes. Their main result is a far-reaching generalization of the Carlitz-Uchiyama bound for the duals of binary BCH codes. In particular, they prove sharp bounds for the generalized Hamming weights of a large class of codes, including duals of BCH codes, classical Goppa codes, Melas codes, and arbitrary cyclic codes of length n=p/sup m/-1. The main tool is the theory of algebraic functions over finite fields, in particular the Hasse-Weil bound for the number of places of degree one. >