Index of bounds on the parameters of codes - Coding Theory

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# 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 *