Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Archive
Cybernetics And Systems Analysis
International Theoretical Science Journal
-->

UDC 519.17
S. Nikolaev1, O. Romanov2, А. Nyshchuk3


1 Defense Intelligence Research Institute, Kyiv, Ukraine

divan24@i.ua

2 Defense Intelligence Research Institute, Kyiv, Ukraine

rolex@i.ua

3 Defense Intelligence Research Institute, Kyiv, Ukraine

svs14@ukr.net

METHOD OF MODIFIED DEPTH GRAPH SEARCH FOR CONSTRUCTING
ALL POSSIBLE GRAY CODES OF A SPECIFIED LENGTH

Abstract. The problem of finding possible variants of the Gray code for the interpretation of time-frequency matrices, which are used in the design of information transmission channels, is considered. An undirected homogeneous incomplete circulant 4-degree graph is constructed. A method and algorithm for implementing a modified search in the graph are proposed, which can be used to construct all the Gray codes of a given length. A formula for calculating the number of variants of these codes is given.

Keywords: bitstream, time-frequency matrix, Gray code, undirected graph.


full text

REFERENCES

  1. Nikolaev S.N., Romanov A.N. Method for recognition of parameters of error-correcting block-cyclic codes by a generator polynomial. Cybernetics and Systems Analysis. 2021. Vol. 57, N 1. P. 146–154. https://doi.org/10.1007/s10559-021-00338-w .

  2. Yerokhin V.F., Roma O.M., Vasylenko S.V., Bezdrabko D.E. Mathematical model of interception of a single jump of a transmitter signal with a PPRF. Bulletin of NTUU "KPI". Radio equipment series. Radio equipment construction. 2016. N 64. P. 75–85. https://doi.org/10.20535/RADAP.2016.64.75-85.

  3. Mutze T., Nummenpalo J. Efficient computation of middle levels Gray codes. ACM Trans. Algorithms. 2018. Vol. 14, Iss. 2. Article 15. https://doi.org/10.1145/3170443.

  4. Beletsky A.Ya. Combinatorics of Gray codes [in Russian]. Kyiv: Izd. comp. "KVIC", 2003. 506 p.

  5. Warren H. Algorithmic tricks for programmers [Russian translation]. Moscow: OOO Dialectika-Williams, 2014. 512 p.

  6. Bitner J.R., Ehrlich G., Reingold E.M. Efficient generation of the binary reflected Gray code and its applications. Comm. ACM. 1976. Vol. 19, N 9. P. 517–521. https://doi.org/10.1145/360336.360343.

  7. Ali Md.M., Islam M.N., Foysal A.B.M. Algorithms for generating binary reflected Gray code sequence: Time efficient approaches. Proc. 2009 International Conference on Future Computer and Communication (03–05 April 2009, Kuala Lumpar, Malaysia). Kuala Lumpar, 2009. P. 79–83. https://doi.org/10.1109/ICFCC.2009.41.

  8. Balakrishnan R., Ranganathan K. A Textbook of Graph Theory. New York: Springer New York, 2012. XIII, 292 p. https://doi.org/10.1007/978-1-4614-4529-6.

  9. Ashraf Iqbal M. Graph Theory and Algorithms. 2010. 522 p.




© 2023 Kibernetika.org. All rights reserved.