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 *