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A Gray code is a cyclic ordering of binary strings so that two successive values differ in only one bit (a Hamming distance of 1).
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New Perfect 2-bit Error Correction Code - Are there any other?
This question was answered by @Noam D. Elkies in the above comments with an excellent link to an article describing the problem.
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New Perfect 2-bit Error Correction Code - Are there any other?
I have recently looked through perfect error correcting codes and found the Hamming(7,3) and Golay(23,7). Using a computer program I have found a new 2 bit perfect error correcting code: Code(90, 2).
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