Construction of I-Deletion-Correcting Ternary Codes

Finding large deletion correcting codes is an important issue in coding theory. Many researchers have studied this topic over the years. Varshamov and Tenegolts constructed the Varshamov-Tenengolts codes (VT codes) and Levenshtein showed the Varshamov-Tenengolts codes are perfect binary one-deletion correcting codes in 1992. Tenegolts constructed T codes to handle the non-binary cases. However the T codes are neither optimal nor perfect, which means some progress can be established. Latterly, Bours showed that perfect deletion-correcting codes have a close relationship with design theory. By this approach, Wang and Yin constructed perfect 5-deletion correcting codes of length 7 for large alphabet size. For our research, we focus on how to extend or combinatorially construct large codes with longer length, few deletions and small but non-binary alphabet especially ternary. After a brief study, we discovered some properties of T codes and produced some large codes by 3 different ways of extending some existing good codes.

Diagrams of cross sections on the Welland Railway, Port Dalhousie

Diagrams of cross sections on the Welland Railway, Port Dalhousie (4 hand-drawn diagrams), March 1860.

Specifications for the erection of a building at Long Point with diagrams

Specifications for the erection of a building at Long Point with diagrams (9 pages, handwritten), n.d.

Diagrams (charts and graphs) made into a booklet with a newspaper cover

Diagrams (charts and graphs) made into a booklet with a newspaper cover. This booklet contains cross sections of the back ditch on the south side of the Welland Canal feeder, west of the Marshville culverts (45 pages, hand drawn). This was created by Fred Holmes, Oct. 3, 1857.