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- W4386875100 abstract "A cross-bifix-free code of length $n$ over $mathbb{Z}_q$ is defined as a non-empty subset of $mathbb{Z}_q^n$ satisfying that the prefix set of each codeword is disjoint from the suffix set of every codeword. Cross-bifix-free codes have found important applications in digital communication systems. One of the main research problems on cross-bifix-free codes is to construct cross-bifix-free codes as large as possible in size. Recently, Wang and Wang introduced a family of cross-bifix-free codes $S_{I,J}^{(k)}(n)$, which is a generalization of the classical cross-bifix-free codes studied early by Lvenshtein, Gilbert and Chee {it et al.}. It is known that $S_{I,J}^{(k)}(n)$ is nearly optimal in size and $S_{I,J}^{(k)}(n)$ is non-expandable if $k=n-1$ or $1leq k<n/2$. In this paper, we first show that $S_{I,J}^{(k)}(n)$ is non-expandable if and only if $k=n-1$ or $1leq k<n/2$, thereby improving the results in [Chee {it et al.}, IEEE-TIT, 2013] and [Wang and Wang, IEEE-TIT, 2022]. We then construct a new family of cross-bifix-free codes $U^{(t)}_{I,J}(n)$ to expand $S_{I,J}^{(k)}(n)$ such that the resulting larger code $S_{I,J}^{(k)}(n)bigcup U^{(t)}_{I,J}(n)$ is a non-expandable cross-bifix-free code whenever $S_{I,J}^{(k)}(n)$ is expandable. Finally, we present an explicit formula for the size of $S_{I,J}^{(k)}(n)bigcup U^{(t)}_{I,J}(n)$." @default.
- W4386875100 created "2023-09-20" @default.
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- W4386875100 date "2023-09-16" @default.
- W4386875100 modified "2023-09-27" @default.
- W4386875100 title "On non-expandable cross-bifix-free codes" @default.
- W4386875100 doi "https://doi.org/10.48550/arxiv.2309.08915" @default.
- W4386875100 hasPublicationYear "2023" @default.
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