Intersections of linear codes #40514
Description
Problem Description
Currently, there is no function to compute the intersection of two linear codes, as another linear code.
Proposed Solution
Add a funtion C1.intersection(C2) that returns the intersection of C1 and C2, as linear codes.
Alternatives Considered
The current easier alternative is to convert everything to vector spaces, compute the intersection, and then construct the corresponding linear code. This can run into an error when the intersection is just 0, as mentioned in #40513.
Additional Information
For this to not run into issues, the zero linear code should be properly handled in Sage, see #40513. This feature could also be used to easily compute the hull of linear codes (the intersection of a code with the dual of another), which is getting a lot of attention recently. This could also be directly implemented as a function C1.hull(C2) (=C1.intersection(C2.dual_code()).
Is there an existing issue for this?
- I have searched the existing issues for a bug report that matches the one I want to file, without success.