THE NEIGHBOR GRAPH OF BINARY SELF-ORTHOGONAL CODES

We define the neighbor graph of binary self-orthogonal codes, where two codes are connected by an edge if they can be reached by the neighbor construction. We show that this graph consists of two connected, regular subgraphs consisting of self-orthogonal codes that contain the all-one vector 1 and self-orthogonal codes that do not contain the all-one vector 1. We count the number of vertices and edges in each and give the degree of the vertices.