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? -- 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.
