# 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} }

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.

## 7 Citations

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

- MathematicsEnumerative 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 ScienceIEEE 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

- MathematicsIEEE 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.

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