Self-Dual Codes over the Integers Modulo 4
Self-Dual Codes over the Integers Modulo 4
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DOI：
10.1016/0097-3165(93)90070-o
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
J. Conway;N. Sloane
中科院分区：
文献类型：
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作者：
J. Conway;N. Sloane
Michael Klemm最近研究了模4整数环Z4上自对偶码的完全重量计数器所满足的条件。在本文中，我们推导出“对称化”权计数器（忽略+1和-1坐标之间的差异）和汉明权计数器的类似定理。我们给出了一些自对偶码的例子，包括实现所有这些定理中出现的基本重量枚举的代码，以及长度为n × 9的自对偶码的完整列表。我们还对由±1 4 O n− 4类型的字生成的自正交码进行了分类。
Michael Klemm has recently studied the conditions satisfied by the complete weight enumerator of a self-dual code over Z 4, the ring of integers modulo 4. In the present paper we deduce analogues theorems for the “symmetrized” weight enumerator (which ignores the difference between+ 1 and− 1 coordinates) and the Hamming weight enumerator. We give a number of examples of self-dual codes, including codes which realize the basic weight enumerators occurring in all these theorems, and the complete list of self-dual codes of length n⩽ 9. We also classify those self-orthogonal codes that are generated by words of type±1 4 O n− 4.