In order to simplify, in a Dowker code with overcrossings and undercrossings denoted we could point out only crossings that differ from a pattern corresponding to the alternating KL with the same numerical code, and denote such crossings with a minus sign. In this case, if we are not trying to distinguish a KL projection from its mirror image, alternating KLs will always be denoted by a Dowker code that contains only positive numbers, and for non-alternating KLs some entries will be negative. For example, to the alternating projection of a figure-eight knot and its mirror image the same code {4},{6,8,2,4} will be assigned; for a non-alternating projection of the knot 8₁₉ and its mirror image the code will be {{8},{12,14,10,-16,4,6,2,-8}}. In the same way, to the non-alternating projection of the link 6₃³ and its mirror image the code {{2,2,2},{8,-10,2,12,6,-4}} will be assigned. The codes obtained will be called DT-codes (where DT comes from Dowker-Thistlethwaite), or Dowker codes in Knotscape notation (according to the computer program Knotscape where that notation is used). 

The relation "over-under" can be easily restored from KL diagrams. Hence, from them you can directly read Gauss and Dowker codes with overcrossings and undercrossings denoted. 

It is important to underline that DT-codes essentially differ from a Dowker code with signs that we will introduce now.

A link projection is called oriented if an orientation is assigned to each component. Let an oriented KL projection L' be given. A vertex will be called negative if it appears in the diagram in the form shown in the following figure (left), and positive if it appears in the form (right). Every vertex of L' belongs to one of the types mentioned. By introducing a simple correspondence "left" (negative), "right" (positive) = "black", "white", we obtain a vertex-colored KL diagram, where every vertex is denoted by a black or white circle. Going further and labelling white (positive) vertices by 1, and black (negative) by -1, we obtain a labelled diagram from which we can directly read a Gauss code with signs (or simply, Gauss code), and a Dowker code with signs (or simply, Dowker code). From here and in the sequel, if there is no other explicit remark, the terms Gauss code and Dowker code will be used only in that sense. Now we have a one-to-one correspondence between oriented KL projections and their Dowker codes. For example, it enables us to distinguish two following composite knots. If we orient them, the Dowker code of the first will be {{6},{4,6,2,10,12,8}}, and the Dowker code of the other {{6},{4,6,2,-10,-12,-8}}.