Codes and Length-Increasing Transitive Binary Relations
Classes of codes defined by binary relations are considered. It turns out that many classes of codes can be defined by length-increasing transitive binary relations. By introducing a general embedding schema we show that the embedding problem can be solved in a unified way for many classes of codes defined in such a way. Several among these classes of codes can be characterized by means of variants of Parikh vectors. This is very useful in constructing many-word concrete codes, maximal codes in corresponding classes of codes. Also, this allows to establish procedures to generate all maximall codes as well as algorithms to embed a code in a maximal one in some classes of codes.
KeywordsCode binary relation embedding problem Parikh vector
Unable to display preview. Download preview PDF.
- 11.Jürgensen, H., Konstatinidis, S.: Codes. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 511–607. Springer, Berlin (1997)Google Scholar
- 18.Shyr, H., Thierrin, G.: Codes and binary relations. In: Lecture Notes 586 “Sèminarie d’Algèbre, Paul Dubreil, Paris, pp. 180–188. Springer, Heidelberg (1975-1976)Google Scholar
- 19.Van Embedding, D.L.: problem for codes defined by binary relations. Preprint 98/A22, Institute of Mathematics, Hanoi (1998)Google Scholar
- 21.Van, D.L., Hung, K.V.: On codes defined by binary relations, Part I: Embedding problem (submitted)Google Scholar
- 22.Van, D.L., Hung, K.V.: On codes defined by binary relations, Part II: Vector characterizations and maximality (submitted)Google Scholar