https://en.wikipedia.org/wiki/Hamming(7,4) ? On Wed, Jan 16, 2019 at 10:34 AM Henry Baker <hbaker1@pipeline.com> wrote:
The simplest form of ECC is that for a single bit:
0 -> 000, 1 -> 111.
The decoding rule is also a simple majority test: 001/010/100 -> 0; 110/101/011 -> 1.
My problem:
I'd like an ECC code that can be computed *linearly* -- i.e., via a (chain of) matrix multiplication(s).
Thus,
codeword . R . P = decodedword
Where R is an invertible matrix and P is some non-invertible matrix -- e.g., a projection matrix.
I haven't been able to find a linear decoding for this version of ECC, nor have I been able to convince myself that it is impossible.
If this type of ECC can't be decoded in a linear fashion, is there any other type of ECC that can?
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