# An Efficient Shift Rule for the Prefer-Max De Bruijn Sequence

## TL;DR

This paper introduces a new, efficient shift rule for generating prefer-max De Bruijn sequences applicable to all sequence orders and alphabets, with an algorithm that is linear in sequence order.

## Contribution

It formulates a universal shift rule for prefer-max De Bruijn sequences and provides a linear-time, memory-efficient algorithm for its implementation.

## Key findings

- The shift rule is applicable to all sequence orders and alphabets.
- The algorithm operates in linear time and memory relative to sequence order.
- The method improves efficiency over previous approaches.

## Abstract

A shift rule for the prefer-max De Bruijn sequence is formulated, for all sequence orders, and over any finite alphabet. An efficient algorithm for this shift rule is presented, which has linear (in the sequence order) time and memory complexity.