## Abstract

We define run sequences of period 2^{<italic>n</italic>} - 1 as the binary sequences where the distribution of runs of 0’s and runs of 1’s is exactly same as that for the maximal length linear shift resister sequences of period 2^{<italic>n</italic>} - 1. We first count the number of all the cyclically distinct run sequences of period 2^{<italic>n</italic>} - 1. For each <italic>n</italic>-tuple, we consider the average number of occurrences over all the run sequences of period 2^{<italic>n</italic>} - 1. We identify the <italic>n</italic>-tuples with average number 1 and, in particular, those that occur exactly once in every run sequence of period 2^{<italic>n</italic>} - 1. We finally prove that, as <italic>n</italic> increases, the average number of every non-zero <italic>n</italic>-tuple approaches to 1.

Original language | English |
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Pages (from-to) | 1 |

Number of pages | 1 |

Journal | IEEE Transactions on Information Theory |

DOIs | |

Publication status | Accepted/In press - 2022 |

### Bibliographical note

Publisher Copyright:IEEE

## All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences