How to list all codewords of C ?

[GUSTAVO TERRA BASTOS]

Hey guys. Hope everyone is fine.

I am sage beginner, I´d like to know how to describe all the codewords from my linear code C. Best, Gustavo.

 

[David Joyner]

Welcome Gustavo!

Here's an example:

sage: C = codes.HammingCode(GF(2),3); C
[7, 4] Hamming Code over GF(2)
sage: C.list()
[(0, 0, 0, 0, 0, 0, 0),
(1, 0, 0, 0, 0, 1, 1),
(0, 1, 0, 0, 1, 0, 1),
(1, 1, 0, 0, 1, 1, 0),
(0, 0, 1, 0, 1, 1, 0),
(1, 0, 1, 0, 1, 0, 1),
(0, 1, 1, 0, 0, 1, 1),
(1, 1, 1, 0, 0, 0, 0),
(0, 0, 0, 1, 1, 1, 1),
(1, 0, 0, 1, 1, 0, 0),
(0, 1, 0, 1, 0, 1, 0),
(1, 1, 0, 1, 0, 0, 1),
(0, 0, 1, 1, 0, 0, 1),
(1, 0, 1, 1, 0, 1, 0),
(0, 1, 1, 1, 1, 0, 0),
(1, 1, 1, 1, 1, 1, 1)]

More info is here
https://wiki.sagemath.org/Coding_Theory
and here
https://groups.google.com/g/sage-coding-theory

- David

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