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Vietnam Journal of Mathematics 39:4 (2011) 425-442

On Codes Defined by Binary Relations

Part II: Characterizations and Maximality

Do Long Van¹ and Kieu Van Hung²

¹Institute of Mathematics, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam

²The Office of Government, 01 Hoang Hoa Tham, Hanoi, Vietnam

Abstract. Superinfix codes (p-superinfix codes, s-superinfix codes), sucypercodes and supercodes have been introduced and considered by the authors in earlier papers. In particular, it has been proved that the embedding problem for these classes of codes has positive solution in both the finite and regular cases. In this paper, characterizations of these codes, especially of the maximal ones, by means of Parikh vectors and their appropriate generalizations are given. Also a procedure to generate all the maximal supercodes on a two-letter alphabet is exhibited.

2000 Mathematics Subject Classification: 94A45, 68Q45.

Keywords: Code, Parikh vector, embedding problem, independent set.

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Published by Springer since January 2013