Index of bounds on the parameters of codesΒΆ
The codes.bounds object may be used to access the bounds that Sage can compute.
| Return an upper bound on the number of codewords in a (possibly non-linear) code. | |
| Delsarte bound on a code with Q matrix  | |
| Find a modified Delsarte bound on additive codes in Hamming space \(H_q^n\) of minimal distance \(d\). | |
| Find the Delsarte bound on a constant weight code. | |
| Find the Delsarte bound on codes in  | |
| Return an upper bound for the dimension of a linear code. | |
| Compute \(E^{w,n}_k(x)\), the Eberlein polynomial. | |
| The asymptotic Elias bound for the information rate. | |
| Return the Elias upper bound. | |
| Compute the entropy at \(x\) on the \(q\)-ary symmetric channel. | |
| Return the Gilbert-Varshamov lower bound. | |
| Return the Griesmer upper bound. | |
| The asymptotic Gilbert-Varshamov bound for the information rate, R. | |
| The Gilbert-Varshamov lower bound for information rate. | |
| The asymptotic Hamming bound for the information rate. | |
| Return the Hamming upper bound. | |
| Compute \(K^{n,q}_l(x)\), the Krawtchouk (a.k.a. Kravchuk) polynomial. | |
| The first asymptotic McEliese-Rumsey-Rodemich-Welsh bound. | |
| The asymptotic Plotkin bound for the information rate. | |
| Return the Plotkin upper bound. | |
| The asymptotic Singleton bound for the information rate. | |
| Return the Singleton upper bound. | |
| 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 *
>>> from sage.all import *
>>> from sage.coding.bounds_catalog import *