On 2013-12-14, Peter Mueller <[email protected]> wrote: > The function delsarte_bound_hamming_space(n, d, q, isinteger=False, > return_data=False, solver='PPL') offers the option isinteger=True. As the > doc doesn't tell it, I got a little curious what is assumed to be integral. > Looking at the implementation it turns out that the distance distribution > is assumed to consist of integers. However, for non-linear codes these > numbers rarely are integral! > > Checking the bounds obtained by this didn't produce anything which > contradicts known lower bounds, but it improves quite a few known upper > bounds in Agrell's and Brouwer's tables (modulo the fact that the MIP > solvers are based on floating point LP solvers and thus don't give proven > results.) > > So I seriously doubt that the isinteger=True is based on a valid > mathematical theorem, or is there some extension of Delsarte's Theorem > which allows to assume that the distance distribution in an optimal code > consists of integers?
No, certainly no such theorem is known. (Lex Scrijver has invented stronger bounds, where one fixes a word, and then one deals with weight distributions relative to this word - but they are no longer LP bounds, but SDP bounds). It's a pure carelessness on my side that led to this bug in the Sage code. Thanks for your report! I've opened a ticket for it: http://trac.sagemath.org/ticket/15520 Best, Dima > > -- Peter Mueller > > -- 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 http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
