On Fri, Apr 16, 2010 at 9:55 AM, Alec Mihailovs <[email protected]> wrote: > On Apr 15, 8:45 am, Andrea Gobbi <[email protected]> wrote: >> Hi! >> I'm using sage for coding theory, and it sems to be great! I have a >> linear code like this: >> MS = MatrixSpace(GF(3),10,27) >> G = MS([ >> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], >> [1,2,0,0,0,0,1,1,2,2,0,0,0,0,1,1,2,2,1,1,1,1,2,2,2,2,0], >> [0,0,1,2,0,0,1,2,1,2,1,1,2,2,0,0,0,0,1,1,2,2,1,1,2,2,0], >> [0,0,0,0,1,2,0,0,0,0,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,0], >> [0,0,0,0,0,0,1,2,2,1,0,0,0,0,0,0,0,0,1,1,2,2,2,2,1,1,0], >> [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,1,1,2,1,2,2,1,2,1,0], >> [0,0,0,0,0,0,0,0,0,0,1,2,2,1,0,0,0,0,1,2,2,1,1,2,2,1,0], >> [1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0], >> [0,0,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0], >> [0,0,0,0,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]]); >> C = LinearCode(G); >> C.dimension(); >> C.length(); >> C.minimum_distance(); >> C.weight_distribution(); >> And I want use the minimum distance (in this case 9) for correct a >> vector with 8 erasures. There are some tools in sage to do this? I try > > If the minimum distance is 9, then, I think, only vectors with 4 > erasures or less can be decoded correctly. Consider, for example, the
I think you meant to say "If the minimum distance is 9, then, I think, only vectors with 4 errors or less can be decoded correctly." I think erasures (where the error positions are assumed to be known) are more complicated. In the example of the last row, if you erase the first 8 0's then the question is are there any other codewords which have the same bits in the non-erased positions. > last row with 5 zeros replaced with ones - if 5 erasures were allowed, > then erasing them, we would get the last row, but erasing 4 remaining > zeros in it instead, we would get the first row - so it couldn't be > uniquely decoded. > > Alec > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
