The Perfect Binary One-Error-Correcting Codes of Length $15$: Part I—Classification
The Perfect Binary One-Error-Correcting Codes of Length $15$: Part I—Classification
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长度为 15 美元的完美二进制纠错码：第一部分——分类
DOI：
10.1109/tit.2009.2027525
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发表时间：
2008
影响因子：
2.5
通讯作者：
Olli Pottonen
中科院分区：
文献类型：
--
作者：
P. Östergård;Olli Pottonen
本文给出了长度为15的最佳二进一纠错码及其长度为16的扩展码的完全分类。有5983个这样的不等价完美码和2165个扩展完美码。这些代码的有效生成依赖于最近的分类斯坦纳四元系统的顺序16。利用Blackmore的结果，对长度为14的最优二进制一纠错码和（15，1024，4）码进行了分类，分别有38408和5983个。
A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5983 such inequivalent perfect codes and 2165 extended perfect codes. Efficient generation of these codes relies on the recent classification of Steiner quadruple systems of order 16. Utilizing a result of Blackmore, the optimal binary one-error-correcting codes of length 14 and the (15, 1024, 4) codes are also classified; there are 38 408 and 5983 such codes, respectively.