关于非等价推广线性扩展完美码的个数
On the number of nonequivalent propelinear extended perfect codes
摘要：
本文证明了存在指数个数的长度增长到无穷大的非等价推广线性扩展完美二元码。具体地说，证明了Potapov所发现的所有可迁扩展完美二元码都是准线性的。所有这些码都具有小的秩，其比相同长度的扩展汉明码的秩多一个。我们调查这些代码的性质，并表明，他们中的任何一个有一个规范化的propelinear表示。
英文摘要：
The paper proves that there exist an exponential number of nonequivalent propelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
