A Gray code for cross-bifix-free sets

Abstract

A cross-bifix-free set of words is a set in which no prefix of any length of any word is the suffix of any other word in the set. A construction of cross-bifix-free sets has recently been proposed by Chee et al. in 2013 within a constant factor of optimality. We propose a trace partitioned Gray code for these cross-bifix-free sets and a CAT algorithm generating it.

Non-overlapping matrices

“…As a further development, it could be interesting to investigate about the possibility to list the matrices in a Gray code sense, following the studies started in [9], [12], [13], [14], [15], where different Gray codes are defined for several set of strings. Clearly, the variable dimension of the matrices has to be considered in a possible definition of a suitable Gray code.…”

“…More recently, cross-bifix-free codes have been deeply studied thanks to their involvement in the development of DNA-based storage systems for big amounts of data [18,19]. In literature several approaches can be found providing different definitions of cross-bifix-free words [7,11,13] and concerning their listing in a Gray code sense [8,9] The generalization of the notion of non-overlapping strings to two dimensions appears, probably for the first time in a rigorous dissertation, in [4] where only square matrices are considered. Here, the notion of prefix or suffix of a string is simply translated into a square matrix anchored in the top-left or bottom-right entry.…”

Konstruksi Kode Cross Bifix Bebas Ternair Berpanjang Genap Untuk Mengatasi Masalah Sinkronisasi Frame

“…Kode ini diklaim menghasilkan kode yang optimal saat panjang katakodenya, yaitu , membagi banyaknya simbol, yaitu . Selain dari [7][8][9][10][11] di atas, konstruksi Kode Cross Bifix Bebas juga diangkat/dibahas dalam [12][13][14] II. METODE Pada bagian ini akan dijelaskan mengenai beberapa definisi dan istilah dalam teori koding yang terkait dengan kode cross bifix bebas.…”

$Q$-ary non-overlapping codes: a generating function approach

“…pattern matching [13], and automata theory [14]. For other related work on fixed-length nonoverlapping codes, see also [11], [15], [16], [17].…”