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 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
