Index of bounds on the parameters of codes¶

The codes.bounds object may be used to access the bounds that Sage can compute.

`codesize_upper_bound()`	Return an upper bound on the number of codewords in a (possibly non-linear) code.
`delsarte_bound_Q_matrix()`	Delsarte bound on a code with Q matrix `q` and lower bound on min. dist. `d`.
`delsarte_bound_additive_hamming_space()`	Find a modified Delsarte bound on additive codes in Hamming space \(H_q^n\) of minimal distance \(d\).
`delsarte_bound_constant_weight_code()`	Find the Delsarte bound on a constant weight code.
`delsarte_bound_hamming_space()`	Find the Delsarte bound on codes in `H_q^n` of minimal distance `d`.
`dimension_upper_bound()`	Return an upper bound for the dimension of a linear code.
`eberlein()`	Compute \(E^{w,n}_k(x)\), the Eberlein polynomial.
`elias_bound_asymp()`	The asymptotic Elias bound for the information rate.
`elias_upper_bound()`	Return the Elias upper bound.
`entropy()`	Compute the entropy at \(x\) on the \(q\)-ary symmetric channel.
`gilbert_lower_bound()`	Return the Gilbert-Varshamov lower bound.
`griesmer_upper_bound()`	Return the Griesmer upper bound.
`gv_bound_asymp()`	The asymptotic Gilbert-Varshamov bound for the information rate, R.
`gv_info_rate()`	The Gilbert-Varshamov lower bound for information rate.
`hamming_bound_asymp()`	The asymptotic Hamming bound for the information rate.
`hamming_upper_bound()`	Return the Hamming upper bound.
`krawtchouk()`	Compute \(K^{n,q}_l(x)\), the Krawtchouk (a.k.a. Kravchuk) polynomial.
`mrrw1_bound_asymp()`	The first asymptotic McEliese-Rumsey-Rodemich-Welsh bound.
`plotkin_bound_asymp()`	The asymptotic Plotkin bound for the information rate.
`plotkin_upper_bound()`	Return the Plotkin upper bound.
`singleton_bound_asymp()`	The asymptotic Singleton bound for the information rate.
`singleton_upper_bound()`	Return the Singleton upper bound.
`volume_hamming()`	Return the number of elements in a Hamming ball.

To import these names into the global namespace, use:

Sage

sage: from sage.coding.bounds_catalog import *

Python

>>> from sage.all import *
>>> from sage.coding.bounds_catalog import *