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() |
Returns 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 *