# A Construction for Balancing Non-Binary Sequences Based on Gray Code Prefixes

## TL;DR

This paper presents a novel method for balancing non-binary sequences using Gray code prefixes, enabling efficient, full encoding and decoding without lookup tables, suitable for very long sequences.

## Contribution

It introduces a generalized construction based on Gray codes for prefix coding that extends Knuth's parallel balancing approach to non-binary sequences.

## Key findings

- Supports very long sequences with full encoding and decoding
- Eliminates the need for lookup tables in encoding
- Allows simple, parallel decoding processes

## Abstract

We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on a generalization of Knuth's parallel balancing approach, which can handle very long information sequences. However, the overall sequence composed of the information sequence, together with the prefix must be balanced. This is reminiscent of Knuth's serial algorithm. The encoding of our construction does not make use of lookup tables, while the decoding process is simple and can be done in parallel.