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: from sage.coding.bounds_catalog import *