Given a length n linear code C over R, construct the subcode of C, generated by the elements specified by the list L, where L is a list of one or more items of the following types:
- (a)
- An element of C;
- (b)
- A set or sequence of elements of C;
- (c)
- A sequence of n elements of R, defining an element of C;
- (d)
- A set or sequence of sequences of type (c);
- (e)
- A subcode of C;
- (f)
- A set or sequence of subcodes of C.
Given a length n linear code C with k generators and an integer t, 1 ≤t < k, return a subcode of C of pseudo-dimension t.
Given a length n linear code C with k generators and a set S of integers, each of which lies in the range [1, k], return the subcode of C generated by the basis elements whose positions appear in S.
> R<w> := GR(4,2); > C := RandomLinearCode(R, 4, 2); > C; (4, 256, 3) Linear Code over GaloisRing(2, 2, 2) Generator matrix: [ 1 0 w + 1 3*w + 2] [ 0 1 3*w + 1 1] > #C; 256 > > C1 := sub< C | 2*C.1, 2*C.2 >; > C1; (4, 16, 3) Linear Code over GaloisRing(2, 2, 2) Generator matrix: [ 2 0 2*w + 2 2*w] [ 0 2 2*w + 2 2] > #C1; 16