Subsections

• The Subcode Constructor
• Sum, Intersection and Dual

Given an [n, k] linear code C, 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:

• An element of C;
• A set or sequence of elements of C;
• A sequence of n elements of K, defining an element of C;
• A set or sequence of sequences of type (c);
• A subcode of C;
• A set or sequence of subcodes of C.

For the following operators, C and D are codes defined as subsets (or subspaces) of the same K-space V.

C + D : Code, Code -> Code

The (vector space) sum of the linear codes C and D, where C and D are contained in the same K-space V.

The intersection of the linear codes C and D, where C and D are contained in the same K-space V.

The dual D of the linear code C. The dual consists of all codewords in the K-space V which are orthogonal to all codewords of C.