单错误校正,双邻接错误检测的最优代码

M. Biberstein, T. Etzion
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引用次数: 11

摘要

在某些存储系统中,最常见的错误是单个错误,其次是物理上存储在内存中相邻位置的两个错误。在这种通信中,我们提出了从这种错误中恢复的最佳代码。我们纠正单个错误并检测双相邻错误。为了检测相邻错误,我们考虑采用字节组织的代码。在二进制的情况下,很明显,代码的长度最多为2/sup r/-r-1,其中r是代码的冗余。我们总结了本案例的已知结果和一些新的结果。对于非二进制的情况,我们给出了这种编码长度的上界,称为“对界”。当且仅当GF(3)上存在具有最小汉明距离5的完美码时,在GF(3)上具有大小为2的字节码才存在。在GF(4)上,对于所有冗余都存在达到字节大小为2的边界的代码。对于大多数其他参数,我们证明了不存在达到界的码。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal codes for single-error correction, double-adjacent-error detection
In certain memory systems the most common error is a single error and the next most common error is two errors in positions which are stored physically adjacent in the memory. In this correspondence we present optimal codes for recovering from such errors. We correct single errors and detect double adjacent errors. For detecting adjacent errors we consider codes which are byte-organized. In the binary case, it is clear that the length of the code is at most 2/sup r/-r-1, where r is the redundancy of the code. We summarize the known results and some new ones in this case. For the nonbinary case we show an upper bound, called "the pairs bound," on the length of such code. Over GF(3) codes with bytes of size 2 which attain the bound exist if and only if perfect codes with minimum Hamming distance 5 over GF(3) exist. Over GF(4) codes which attain the bound with byte size 2 exist for all redundancies. For most other parameters we prove the nonexistence of codes which attain the bound.
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