def codesize_upper_bound(n, d, q, algorithm=None):
r"""
This computes the minimum value of the upper bound using the
methods of Singleton, Hamming, Plotkin, and Elias.
If algorithm="gap" then this returns the best known upper
bound `A(n,d)=A_q(n,d)` for the size of a code of length n,
minimum distance d over a field of size q. The function first
checks for trivial cases (like d=1 or n=d), and if the value
is in the built-in table. Then it calculates the minimum value
of the upper bound using the algorithms of Singleton, Hamming,
Johnson, Plotkin and Elias. If the code is binary,
`A(n, 2\ell-1) = A(n+1,2\ell)`, so the function
takes the minimum of the values obtained from all algorithms for the
parameters `(n, 2\ell-1)` and `(n+1, 2\ell)`. This
wraps GUAVA's (i.e. GAP's package Guava) UpperBound( n, d, q ).
If algorithm="LP" then this returns the Delsarte (a.k.a. Linear
Programming) upper bound.
EXAMPLES::
sage: codesize_upper_bound(10,3,2)
93
sage: codesize_upper_bound(24,8,2,algorithm="LP")
4096
sage: codesize_upper_bound(10,3,2,algorithm="gap") # optional - gap_packages (Guava package)
85
sage: codesize_upper_bound(11,3,4,algorithm=None)
123361
sage: codesize_upper_bound(11,3,4,algorithm="gap") # optional - gap_packages (Guava package)
123361
sage: codesize_upper_bound(11,3,4,algorithm="LP")
109226
"""
if algorithm == "gap":
gap.load_package('guava')
return int(gap.eval("UpperBound(%s,%s,%s)" % (n, d, q)))
if algorithm == "LP":
return int(delsarte_bound_hamming_space(n, d, q))
else:
eub = elias_upper_bound(n, q, d)
gub = griesmer_upper_bound(n, q, d)
hub = hamming_upper_bound(n, q, d)
pub = plotkin_upper_bound(n, q, d)
sub = singleton_upper_bound(n, q, d)
return min([eub, gub, hub, pub, sub])
def codesize_upper_bound(n, d, q, algorithm=None):
r"""
This computes the minimum value of the upper bound using the
methods of Singleton, Hamming, Plotkin, and Elias.
If algorithm="gap" then this returns the best known upper
bound `A(n,d)=A_q(n,d)` for the size of a code of length n,
minimum distance d over a field of size q. The function first
checks for trivial cases (like d=1 or n=d), and if the value
is in the built-in table. Then it calculates the minimum value
of the upper bound using the algorithms of Singleton, Hamming,
Johnson, Plotkin and Elias. If the code is binary,
`A(n, 2\ell-1) = A(n+1,2\ell)`, so the function
takes the minimum of the values obtained from all algorithms for the
parameters `(n, 2\ell-1)` and `(n+1, 2\ell)`. This
wraps GUAVA's (i.e. GAP's package Guava) UpperBound( n, d, q ).
If algorithm="LP" then this returns the Delsarte (a.k.a. Linear
Programming) upper bound.
EXAMPLES::
sage: codes.bounds.codesize_upper_bound(10,3,2)
93
sage: codes.bounds.codesize_upper_bound(24,8,2,algorithm="LP")
4096
sage: codes.bounds.codesize_upper_bound(10,3,2,algorithm="gap") # optional - gap_packages (Guava package)
85
sage: codes.bounds.codesize_upper_bound(11,3,4,algorithm=None)
123361
sage: codes.bounds.codesize_upper_bound(11,3,4,algorithm="gap") # optional - gap_packages (Guava package)
123361
sage: codes.bounds.codesize_upper_bound(11,3,4,algorithm="LP")
109226
"""
if algorithm == "gap":
gap.load_package("guava")
return int(gap.eval("UpperBound(%s,%s,%s)" % (n, d, q)))
if algorithm == "LP":
return int(delsarte_bound_hamming_space(n, d, q))
else:
eub = elias_upper_bound(n, q, d)
gub = griesmer_upper_bound(n, q, d)
hub = hamming_upper_bound(n, q, d)
pub = plotkin_upper_bound(n, q, d)
sub = singleton_upper_bound(n, q, d)
return min([eub, gub, hub, pub, sub])