On Thursday, October 6, 2016 at 5:10:55 PM UTC+2, David Joyner wrote: > > On Thu, Oct 6, 2016 at 11:03 AM, Giorgos Marios <[email protected] > <javascript:>> wrote: > > I am sorry, i want a large linear code capable of correcting t errors so > i > > can experiment with a simple McEliece implementation without using goppa > > codes. > > I am searching many hours for the right code family and the code > > constructors of sage without any luck. >
McEliece works with any code family for which you have an efficient decoding algorithm. Sage can out-of-the-box efficiently decode Reed-Solomon codes, so that's an obvious choice. The classical McEliece scheme uses binary Goppa codes. These are subfield subcodes of Reed-Solomon codes, so using the `SubfieldSubcode` construction, Sage can decode those out-of-the-box as well (however, one must be careful about which Reed-Solomon code one takes). Another obvious choice is, as David suggests, BCH codes which are subfield subcodes of "classical" Reed-Solomon codes, i.e. where the evaluation points form a multiplicative group. Be aware that the current implementation of BCH Codes in Sage does not give you an efficient decoder, since it "doesn't know" it's a subfield subcode of an RS code. There is work-in-progress on such an implementation of BCH codes on Trac: https://trac.sagemath.org/ticket/20335, but it's probably not yet ready for prime-time. See also https://trac.sagemath.org/ticket/21352 for an in-progress implementation of getting a working McEliece implementation into Sage. -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
