Index of bounds on the parameters of codesΒΆ

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

codesize_upper_bound() Returns an upper bound on the number of codewords in a (possibly non-linear) code.
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_hamming_space() Find the Delsarte bound [De1973] on codes in Hamming space H_q^n of minimal distance d
dimension_upper_bound() Return an upper bound for the dimension of a linear code.
elias_bound_asymp() The asymptotic Elias bound for the information rate.
elias_upper_bound() Returns the Elias upper bound.
entropy() Computes the entropy at \(x\) on the \(q\)-ary symmetric channel.
gilbert_lower_bound() Returns the Gilbert-Varshamov lower bound.
griesmer_upper_bound() Returns 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() Returns 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() Returns the Plotkin upper bound.
singleton_bound_asymp() The asymptotic Singleton bound for the information rate.
singleton_upper_bound() Returns the Singleton upper bound.
volume_hamming() Returns the number of elements in a Hamming ball.

Note

To import these names into the global namespace, use:

sage: from sage.coding.bounds_catalog import *