On Friday, July 8, 2016 at 11:52:11 AM UTC-7, Dima Pasechnik wrote: > > > No, because there is no concept of "short vector" that behaves > sufficiently well. > > it is not 100% true; Z_7 is a field, thus you get a vector space, and a > coding theory-like problem > of finding a some sort of measure to see how far apart two vectors are. > For instance it can be Hamming distance (# of coordinates in which two > vectors differ), > and then it's the classical coding theory setup. >
The key is in the "sufficiently well". If you could find a (positive definite) quadratic form that induces the Hamming weight (note it's called a weight, not a norm!) then we could use Gramm-Schmidt orthogonalization (we wouldn't even need LLL because we're working over a field!). That would probably solve the decoding problem quite efficiently. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
