报告题目 (Title)：通过可扩展码构造不可扩展的cross-bifix-free码 (Constructions of non-expandable cross-bifix-free codes via expandable codes)
报告人 (Speaker)： 陈博聪 教授（华南理工大学）
报告时间 (Time)：2024年11月15日(周五) 10:00
报告地点 (Place)：腾讯会议 509-150-895
邀请人(Inviter)：丁洋
主办部门：理学院数学系
报告摘要：:A cross-bifix-free code of length $n$ over $\mathbb{Z}_q$ is a non-empty subset of $\mathbb{Z}_q^n$ such that the prefix set of each codeword is disjoint from the suffix set of every codeword. To achieve good performance in communication systems, it is desirable to construct cross-bifix-free codes with large size. Recently, Wang and Wang generalized the classical cross-bifix-free codes presented by Levenshtein, Gilbert and Chee {\it et al.} by constructing a new family of cross-bifix-free codes $S_{I,J}^{(k)}(n)$. The code $S_{I,J}^{(k)}(n)$ is nearly optimal in terms of its size and non-expandable if $k=n-1$ or $1\leq k<n/2$. There are three major ingredients in this talk. The first is to improve the results in [Chee {\it et al.}, IEEE-TIT, 2013] and [Wang and Wang, IEEE-TIT, 2022] in which we prove that the code $S_{I,J}^{(k)}(n)$ is non-expandable if and only if $k=n-1$ or $1\leq k<n/2$. The second ingredient contributes to a new family of cross-bifix-free codes $U^{(t)}_{I,J}(n)$. This new code enables us to construct non-expandable cross-bifix-free codes $S_{I,J}^{(k)}(n)\bigcup U^{(t)}_{I,J}(n)$ whenever $S_{I,J}^{(k)}(n)$ is expandable. The union of $U^{(t)}_{I,J}(n)$ and $S_{I,J}^{(k)}(n)$ enlarges the size of $S_{I,J}^{(k)}(n)$. Finally, we give an explicit formula for the size of $S_{I,J}^{(k)}(n)\bigcup U^{(t)}_{I,J}(n)$. This talk is based on a joint work with Gaojun Luo and Chunyan Qin.
