Keywords and phrases: AUNU numbers, set theory, set inclusion, coding theory, perfect codes, word length, transmission errors.
Received: December 15, 2023; Revised: March 28, 2024; Accepted: April 14, 2024; Published: June 17, 2024
How to cite this article: P. B. Chun, N. Jeltel, N. M. Kamoh and S. Abah, Error detection and correction of the [15 8 3]-perfect code due to the AUNU avoiding permutation patterns, Universal Journal of Mathematics and Mathematical Sciences 20(1) (2024), 39-47. https://doi.org/10.17654/2277141724004
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References: [1] Noga Alon and Andy Liu, An application of set theory to coding theory, Math. Mag. 62(4) (1989), 233-237. http://www.jstor.org/stable/2689761. [2] Robert. J. McEliece, The Theory of Information and Coding, 2nd ed, Cambridge University Press, UK, 2004, pp. 1-2. [3] A. A. Ibrahim, P. B. Chun and N. M. Kamoh, A new [14 8 3]-linear code from the AUNU generated [7 4 2]-linear code and the known [7 4 3] Hamming code using the construction, J. Comput. Appl. Math. 7 (2017), 379-381. DOI: 10.4172/2168- 9679.1000379. [4] P. B. Chun, A. A. Ibrahim, M. S. Magami and D. D. Wisdom, On a non-trivial [15 8 3] perfect code due to the non-associative property of (123)-avoiding class of AUNU permutation patterns, Journal of Mathematics and Statistics Science 1(1) (2018), 8-10. [5] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-correcting Codes, North-Holland, Amsterdam, 1977, pp. 372-377. [6] P. Frankl and J. Pach, On the number of sets in a null t-design, European Journal of Combinatorics 4 (1982), 21-23. [7] D. E. Muller, The applications of Boolean algebra to switching circuits design and to error detection, IRE Transactions EC-3 (1954), 6-12. [8] J. F. Humphreys and M. Y. Prest, Numbers, Groups and Codes, 2nd ed., Cambridge University Press, 2004, pp. 96-98. [9] Kenneth H. Rosen, Discrete Mathematics and its Applications, 7th ed., McGraw Hill, 2012, pp. 115-116. [10] A. A. Ibrahim, On wreath product of permutation groups and algebraic theoretic properties of Bara’at Al-Dhimmah models, Usmanu Danfodiyo University, Sokoto, PhD Thesis, 2005. [11] A. A. Ibrahim et al., Integer Sequence A123642 Online Encyclopedia of Integer sequence, 2006. http://www.research.att.com/~njas/sequence/?q=123642&sort=0&language= english&go=search. [12] A. A. Ibrahim et al., Integer Sequence A128929 Online Encyclopedia of Integer sequence, 2007. http://www.research.att.com/~njas/sequence/?q=128929&sort=0&language= english&go=search. [13] A. A. Ibrahim et al., Integer Sequence A128984 Online Encyclopedia of Integer sequence, 2007. http://www.research.att.com/~njas/sequence/?q=18984&sort=0&language= english&go=search.
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