An Extension Theorem for Linear Codes
An Extension Theorem for Linear Codes
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线性码的可拓定理
DOI：
10.1023/a:1008319024396
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
R. Hill
中科院分区：
文献类型：
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作者：
R. Hill
最小距离为奇数的二元线性[n，k，d]码可以推广到[n+1，k，d+1]码，这是编码理论中遇到的第一个结果。这是关于二进制码的为数不多的基本结果之一，它不是对Toq-ary码的明显推广。本文的目的是给出Aq元[n，k，d]码可扩张为[n+1，k，d+1]码的一个简单的充分条件。应用于良码的构造和分类，证明某些码的不存在，以及在有限几何中的应用。
One of the first results one meets in coding theory is that a binary linear [n,k,d] code, whose minimum distance is odd, can be extended to an [n+ 1,k,d+ 1] code. This is one of the few elementary results about binary codes which does not obviously generalise toq-ary codes. The aim of this paper is to give a simple sufficient condition for aq-ary [n,k,d] code to be extendable to an [n+ 1,k,d+ 1] code. Applications will be given to the construction and classification of good codes, to proving the non- existence of certain codes, and also an application in finite geometry.