#12418: adding Delsarte bound for codes
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Reporter: dimpase | Owner: wdj
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.4
Component: coding theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: #12533 | Stopgaps:
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Comment (by ppurka):
I think the `Krawtchouk` polynomial could be computed explicitly by not
making repeated calls to `binomial`. This should speed it up. I have
something like this in mind:
{{{
def Krawtchouk2(n,q,l,i):
# Use the expression in equation (55) of MacWilliams & Sloane, pg 151
# We write jth term = some_factor * (j-1)th term
kraw = jth_term = (q-1)**l * binomial(n, l) # j=0
for j in range(1,l+1):
jth_term *= -q*(l-j+1)*(i-j+1)/((q-1)*j*(n-j+1))
kraw += jth_term
return kraw
n,q,l,i = 10,8,7,5
timeit('Krawtchouk2(n,q,l,i)')
timeit('Krawtchouk (n,q,l,i)')
print Krawtchouk2(n,q,l,i) == Krawtchouk(n,q,l,i)
625 loops, best of 3: 53.3 µs per loop
625 loops, best of 3: 205 µs per loop
True
}}}
I noticed that sage handles nonintegral components in the binomial, so the
expression for the `Krawtchouk` already works with nonintegral `n` and
`x`.
{{{
n,q,l,i = 10.6,8,7,5.4
#timeit('Krawtchouk3(n,q,l,i)')
timeit('Krawtchouk2(n,q,l,i)')
timeit('Krawtchouk (n,q,l,i)')
print Krawtchouk2(n,q,l,i) == Krawtchouk(n,q,l,i)
print Krawtchouk2(n,q,l,i), Krawtchouk(n,q,l,i)
625 loops, best of 3: 382 µs per loop
125 loops, best of 3: 4.74 ms per loop
False
93582.0160001147 93582.0159999999
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12418#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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