On 12/15/2013 03:01 PM, P Purkayastha wrote:
On 12/15/2013 06:46 AM, Peter Mueller 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!
I think isinteger probably makes sense for the
delsarte_bound_additive_hamming_space() function.
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.)
The LP solver used should give exact results and not have any floating
point problems. See http://trac.sagemath.org/ticket/12533
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
I am not sure why there would be improvements to the tables. Someone
would have noticed such improvements earlier, right? The result obtaind
from allowing isinteger=True should be an upper bound to the actual
maximization problem. This is because putting isinteger=True imposes
more constraints on the variables (the distance distribution) and so the
result obtained from setting this to true should be at least as large as
the result obtained from setting this to false (since the constraint
space is larger in the latter case).
Can you perhaps give an example where setting isinteger=True gives a
bigger number than when setting isinteger=False?
Sorry, my question was (obviously) the opposite - when does
isinteger=True give a *smaller* number compared to isinteger=False.
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