Re: [math-fun] *linear* decoding of ECC code ?

On Wed, Jan 16, 2019 at 11:25 AM Adam P. Goucher <apgoucher@gmx.com> wrote:

Hamming(7, 4) has linear encoding, but not linear decoding. For example:

0000 encodes to 0000000

which means (with the error-correcting property) that:

0000001 decodes to 0000 0000010 decodes to 0000 0000100 decodes to 0000 0001000 decodes to 0000 0010000 decodes to 0000 0100000 decodes to 0000 1000000 decodes to 0000

If the decoding function were linear, it would therefore be identically zero (which it isn't).

OK, I see. The syndrome is a linear function of the codewords, but the data is not. Thanks! -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com