We initiate the study of self-dual codes over GF(4) whose corresponding graphs have fixed rankwidth. We show that by combining the structural properties of rankwidth 1 graphs, the classification of corresponding codes becomes significantly faster.
We give a new algorithm for computing weight enumerators using Binary Decision Diagrams (BDD), which has similar complexity to brute force O(2^k) but has the benefit that we automatically get complexity O(2^min{k,n−k}) (for k > n/2) without needing to consider the dual code.
We show that the minimum distance of a code is at least 3 if and only if the corresponding graph does not contain any pendant vertex or any twin-pairs. We also give an algorithm for computing an approximate minimum distance in codes corresponding to general graphs.