Hello, as David correctly pointed out, MAGMA does have quite efficient algorithms for computing the minimum distance of block codes over finite fields, not only for linear, but also for additive codes.
But David isn't right in his assumption that I would have implemented the algorithms in MAGMA. The actual version of the algorithms is due to Greg White, building upon e.g. efficient algorithms for finite fields and vectors spaces. Other people who made major contribution to MAGMA's coding theory package are Allan Steel, Damien Fisher, and John Cannon. I have contribution some of the ideas used in the algorithms, but not all all. We have also been improving algorithms by Brouwer and Zimmermann for general codes, as well as special algorithms for cyclic codes. Greg White developed special algorithms for quasicyclic code. So indeed Magma first checks for the type of a code and the uses the suitable algorithm. My knowledge of GAP is rather restricted, but as pointed out before, MAGMA's efficient algorithms for computations in finite fields and vector spaces are at the core of the good performance. It is possible to enumerate more than 2^23 codewords per second. You can get more information at http://magma.maths.usyd.edu.au/ Markus David Joyner wrote: > 3. MAGMA's algorithm is faster and more sophisticated but you can't read the > C code anywhere as far as I know. Some hints are in some talks by > Markus Grassl http://iaks-www.ira.uka.de/home/grassl/ who I think writes > most > of their coding theory programs. I get the impression that it first > dicides what kind of code it > is (cyclic, for example), then puts the code in "standard form", then > (if the > code is long, ie n is large compared to k) it plays some tricks with the > generator matrix. > These tricks are described in his paper "Searching for good linear > codes" which > you can find it here: > http://iaks-www.ira.uka.de/home/grassl/Academia/Algo-Gruppen-Codes-2003/ > I actually thought of this trick before I read his paper but could not > get a fast > or elegant implementation working in GAP. I thnk he deserves a lot of > credit for making > it work so fast and writing such a nice description of the idea. > > ++++++++++++++++++++++++++++++++++++++++++++++++++++ > > Pere Urbón Bayes wrote: > > Hello to every body, I know that this problem is NP ... but how about > > the existing algorism? Is there any thing?. I mean this because one of > > my interest in sage will be to provide our software with a lib that > > could work eficiently with this problem. > > > > Regards, > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
