Generating m-Ary Gray Codes and Related Algorithms-Reference-Cited by-同舟云学术

Generating m-Ary Gray Codes and Related Algorithms

Published:2024-07-13 Issue:7 Volume:17 Page:311
ISSN:1999-4893
Container-title:Algorithms
language:en
Short-container-title:Algorithms

Author:

Bouyuklieva Stefka¹^ORCID,Bouyukliev Iliya²^ORCID,Bakoev Valentin¹^ORCID,Pashinska-Gadzheva Maria²^ORCID

Affiliation:

1. Faculty of Mathematics and Informatics, St. Cyril and St. Methodius University of Veliko Tarnovo, 5000 Veliko Tarnovo, Bulgaria

2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 5000 Veliko Tarnovo, Bulgaria

Abstract

In this work, we systematize several implementations of the Gray code over an alphabet with m≥2 elements, which we present in C code so that they can be used directly after copying from the text. We consider two variants—reflected and modular (or shifted) m-ary Gray codes. For both variants, we present the ranking and unranking functions, as well as algorithms for generating only a part of the code, more precisely the codewords between two given vectors. Finally, we give algorithms that generate a maximal set of non-proportional vectors of length n over the given alphabet in a Gray code.

Funder

Bulgarian National Science Fun

Publisher

MDPI AG

Link

https://www.mdpi.com/1999-4893/17/7/311/pdf

Reference14 articles.

1. Gray, F. (1953). Pulse Code Communication. (2,632,058), U.S. Patent.

2. Knuth, D. (2014). The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1, Addison-Wesley.

3. On m-ary Gray codes;Sharma;Inf. Sci.,1978

4. On Generating the N-ary Reflected Gray Codes;Er;IEEE Trans. Comput.,1984

5. Q-ary Gray codes and weight distributions;Gulliver;Appl. Math. Comput.,1999