tailieunhanh - Báo cáo toán học: " An Embedding Algorithm for Supercodes and Sucypercodes Kieu Van Hung and Nguyen Quy Khang Hanoi Pedagogical "

Supercodes và sucypercodes, các trường hợp cụ thể của hypercodes, đã được giới thiệu và xem xét DL Văn và là tác giả đầu tiên của bài viết này. Đặc biệt, nó đã được chứng minh rằng, cho các lớp học của mã số, vấn đề nhúng có giải pháp tích cực. | Vietnam Journal of Mathematics 33 2 2005 199-206 V Í e It ini ai m J o mt r im ai I of MATHEMATICS VAST 2005 An Embedding Algorithm for Supercodes and Sucypercodes Kieu Van Hung and Nguyen Quy Khang Hanoi Pedagogical University No. 2 Phuc Yen Vinh Phuc Vietnam Received July 21 2004 Revised October 15 2004 Abstract. Supercodes and sucypercodes particular cases of hypercodes have been introduced and considered by D. L. Van and the first author of this paper. In particular it has been proved that for such classes of codes the embedding problem has positive solution. Our aim in this paper is to propose another embedding algorithm which in some sense is simpler than those obtained earlier. 1. Preliminaries . p. .p. .embedding problem. 200 Kieu Van Hung and Nguyen Quy Khang . . . . . . . . . .length. . .code. . 1. . 1 2 . . 1 2 . . . .maximal. maximal in C infix. factor . . .proper. infix code Xf . .subword. . 1 . x 0 1 1 .1. . 0. . x 0 . .proper subword. hypercode . .permutation. I. .cyclic permutation. Definition . A subset of is a supercode sucypercode over if no word in is a proper subword of a permutation cyclic permutation resp. of another word in it. Denote by C . and C . the classes of all supercodes and sucypercodes over respectively. Example . .2. .2. .. XX. . . . 22 22 32 3 An Embedding Algorithm for Supercodes and Sucypercodes 201 2 . substitution. . .. .homomorphism . . A . A AAAAAAAAAAAAA A 1 A A 2 AAAAAA AAAAAAA A 1 A A A AhArA A 1 . A AAraAA . A .- 2 2 2 A A . AAAAaAAAA A AAAAAAAAAAA A AA AAAA AA AAAArrAAAAA AA AAAAArA AA AA . .-1. . .2. . . . . . .- . .A .-1 . . . A . .A A -. . A 1. . . A - . A -1. A -1. . Theorem . The embedding problem has positive answer in the finite case for every class C . of codes . More precisely every finite code . in . with . is included in a code which is maximal in C . and remains finite with. Namely can be computed by the following formulas according to the case. A For .