<i>Q</i>-Ary Non-Overlapping Codes: A Generating Function Approach
نویسندگان
چکیده
Non-overlapping codes are a set of codewords in $\bigcup _{n \ge 2} \mathbb {Z}_{q}^{n}$ , where notation="LaTeX">$\mathbb {Z}_{q} = \{0,1, {\dots },q-1\}$ such that the prefix each codeword is not suffix any set, including itself; and for variable-length codes, does contain other as subword. In this paper, we investigate generic method to generalize binary notation="LaTeX">$q$ -ary ones notation="LaTeX">$q > 2$ analyze generalization on two constructions given by Levenshtein (also Gilbert; Chee, Kiah, Purkayastha, Wang) Bilotta, respectively. The former construction gives large non-expandable fixed-length non-overlapping whose size can be explicitly determined; latter first attempt generate codes. More importantly, allows us utilize generating function approach cardinality underlying only enables derive new results, e.g., recurrence relations their cardinalities, combinatorial interpretations constructions, superior limit cardinalities some special cases, but also greatly simplifies arguments these results. Furthermore, give an exact formula number words do code subwords. This thereby solves open problem Bilotta induces recursive upper bound maximum
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2022
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2022.3167845