Improved Methods For Generating Quasi-Gray Codes

TL;DR

This paper introduces new algorithms for generating quasi-Gray codes that optimize the number of bits read and written, improve average efficiency, and increase the total number of generated strings, advancing the state of the art.

Contribution

It presents a trade-off framework and novel algorithms that outperform previous methods in efficiency and code length for quasi-Gray code generation.

Findings

Algorithms read fewer bits on average

Increased number of generated bit strings

Reduced bits written per step

Abstract

Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering the number of bits read and written at each generating step, the average number of bits read while generating the entire code, and the number of strings generated in the code. Our results give a trade-off between these constraints, and present algorithms that do less work on average than previous results, and that increase the number of bit strings generated.