On the Classification and Enumeration of Self-Dual Codes
On the Classification and Enumeration of Self-Dual Codes
复制标题
DOI：
10.1016/0097-3165(75)90042-4
复制
发表时间：
1975-05
期刊：
影响因子：
--
通讯作者：
V. Pless;N. Sloane
中科院分区：
文献类型：
--
作者：
V. Pless;N. Sloane
本文给出了所有[22，11]和[24，12]二元自对偶码的一个完全分类。对于每一个代码，我们给出了它的组的顺序，与它等价的代码的数量，以及它的权重分布。存在唯一的[24，12，6]自对偶码。使用了关于自对偶码计数的几个定理，包括最小距离为n × 4的码的个数公式，以及所有长度为n的码的重量计数器之和的公式。对由权值为4的码字生成的自正交码进行了完全刻画。
A complete classification is given of all [22, 11] and [24, 12] binary self-dual codes. For each code we give the order of its group, the number of codes equivalent to it, and its weight distribution. There is a unique [24, 12, 6] self-dual code. Several theorems on the enumeration of self-dual codes are used, including formulas for the number of such codes with minimum distance ⩾ 4, and for the sum of the weight enumerators of all such codes of lengthn. Selforthogonal codes which are generated by code words of weight 4 are completely characterized.