# Variable-Length Non-Overlapping Codes

```@article{Bilotta2017VariableLengthNC,
title={Variable-Length Non-Overlapping Codes},
author={Stefano Bilotta},
journal={IEEE Transactions on Information Theory},
year={2017},
volume={63},
pages={6530-6537}
}```
• S. Bilotta
• Published 12 May 2016
• Computer Science
• IEEE Transactions on Information Theory
We define a variable-length code having the property that no (non-empty) prefix of each its codeword is a suffix of any other one, and vice versa. This kind of code can be seen as an extension of two well-known codes in the literature, called, respectively, fix-free code and non-overlapping code. In this paper we present constructive algorithms for such codes and some numerical results about their cardinality.
Variable dimension non-overlapping matrices
• Computer Science
• 2020
This paper uses non-overlapping variable length strings as rows of the matrices and imposing the avoidance of two consecutive patterns of length k, gets the desired sets of non-ovelapping matrices with variable dimension.
Non-overlapping matrices via Dyck words
• Mathematics
Enumerative Combinatorics and Applications
• 2021
We define a set of binary matrices where any two of these can not be placed one on another such that the corresponding entries coincide. The rows of the matrices are obtained by means of Dyck words.
Non-overlapping Dyck matrices
• Mathematics
• 2018
We define a set of binary matrices where any two of them can not be placed one on the other in a way such that the corresponding entries coincide. The rows of the matrices are obtained by means of
Q-ary non-overlapping codes: a generating function approach
• Computer Science
IEEE Trans. Inf. Theory
• 2022
An exact formula is given for the number of fixed-length words that do not contain the codewords in a variable-length non-overlapping code as subwords that thereby solves an open problem by Bilotta and induces a recursive upper bound on the maximum size of variable- length non- overlapping codes.
A construction for variable dimension strong non-overlapping matrices
• Mathematics, Computer Science
• 2022
We propose a method for the construction of sets of variable dimension strong non-overlapping matrices basing on any strong non-overlapping set of strings.
Mutual Borders and Overlaps
• D. Gabric
• Mathematics
IEEE Transactions on Information Theory
• 2022
This paper gives a recurrence for the number of mutually bordered pairs of words and shows that the expected shortest overlap between pairs of Words is bounded above by a constant.
A Strong Non-overlapping Dyck Code
• Computer Science
DLT
• 2021