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() 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 *