Binary Perfect Codes of Length 15 by the Generalized Concatenated Construction

被引：5
|
作者：
V. A. Zinoviev
D. V. Zinoviev
机构：
[1] RAS,Institute for Information Transmission Problems
来源：
Problems of Information Transmission | 2004年 / 40卷 / 1期
关键词：
System Theory; Generalize Concatenate; Perfect Code; Binary Perfect Code; Concatenate Construction;
D O I：
10.1023/B:PRIT.0000024877.03232.39
中图分类号：
学科分类号：
摘要：
We enumerate binary nonlinear perfect codes of length 15 obtained by the generalized concatenated (GC) construction. There are 15 different types of such codes. They are defined by pairs of MDS codes Ai: (4, 2, 64)4. For every pair we give the number of nonequivalent codes of this type. In total, there are 777 nonequivalent binary perfect codes of length 15 obtained by the GC construction. This number includes the Hamming code (of rank 11), 18 Vasil'ev codes (of rank 12), and 758 codes of rank 13.
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页码：25 / 36
页数：11
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