  In this paper, we study binary triorthogonal codes and their relation to
CSS-T quantum codes. We characterize the binary triorthogonal codes that are
minimal or maximal with respect to the CSS-T poset, and we also study how to
derive new triorthogonal matrices from existing ones. Given a binary
triorthogonal matrix, we characterize which of its equivalent matrices are also
triorthogonal. As a consequence, we show that a binary triorthogonal matrix
uniquely determines the parameters of the corresponding triorthogonal quantum
code, meaning that any other equivalent matrix that is also triorthogonal gives
rise to a triorthogonal quantum code with the same parameters.
