Index of boundsΒΆ
The codes.bounds
object may be used to access the bounds that Sage can compute.
codesize_upper_bound() |
This computes the minimum value of the upper bound using the methods of Singleton, Hamming, Plotkin, and Elias. |
dimension_upper_bound() |
Returns an upper bound \(B(n,d) = B_q(n,d)\) for the dimension of a linear code of length n, minimum distance d over a field of size q. Parameter “algorithm” has the same meaning as in codesize_upper_bound() |
elias_bound_asymp() |
Computes the asymptotic Elias bound for the information rate, provided \(0 < \delta < 1-1/q\). |
elias_upper_bound() |
Returns the Elias upper bound for number of elements in the largest code of minimum distance d in \(\GF{q}^n\). Wraps GAP’s UpperBoundElias. |
entropy() |
Computes the entropy at \(x\) on the \(q\)-ary symmetric channel. |
gilbert_lower_bound() |
Returns lower bound for number of elements in the largest code of minimum distance d in \(\GF{q}^n\). |
griesmer_upper_bound() |
Returns the Griesmer upper bound for number of elements in the largest code of minimum distance d in \(\GF{q}^n\). Wraps GAP’s UpperBoundGriesmer. |
gv_bound_asymp() |
Computes the asymptotic GV bound for the information rate, R. |
gv_info_rate() |
GV lower bound for information rate of a q-ary code of length n minimum distance delta*n |
hamming_bound_asymp() |
Computes the asymptotic Hamming bound for the information rate. |
hamming_upper_bound() |
Returns the Hamming upper bound for number of elements in the largest code of minimum distance d in \(\GF{q}^n\). Wraps GAP’s UpperBoundHamming. |
mrrw1_bound_asymp() |
Computes the first asymptotic McEliese-Rumsey-Rodemich-Welsh bound for the information rate, provided \(0 < \delta < 1-1/q\). |
plotkin_bound_asymp() |
Computes the asymptotic Plotkin bound for the information rate, provided \(0 < \delta < 1-1/q\). |
plotkin_upper_bound() |
Returns Plotkin upper bound for number of elements in the largest code of minimum distance d in \(\GF{q}^n\). |
singleton_bound_asymp() |
Computes the asymptotic Singleton bound for the information rate. |
singleton_upper_bound() |
Returns the Singleton upper bound for number of elements in the largest code of minimum distance d in \(\GF{q}^n\). Wraps GAP’s UpperBoundSingleton. |
volume_hamming() |
Returns number of elements in a Hamming ball of radius r in \(\GF{q}^n\). Agrees with Guava’s SphereContent(n,r,GF(q)). |
Note
To import these names into the global namespace, use:
sage: from sage.coding.bounds_catalog import *