A [49 16 6 ]-Linear Code as Product Of The [7 4 2 ] Code Due to Aunu and the Hamming [7 4 3 ] Code

Volume 4, Issue 3, Article 4 - 2018

Authors: CHUN, Pamson Bentse; IBRAHIM Alhaji Aminu; MAGAMI, Mohe'd Sani

Copyright © 2018 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

The enumeration of the construction due to "Audu and Aminu"(AUNU) Permutation patterns, of a [ 7 4 2 ]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code has been reported by the Authors. The [ 7 4 2 ] linear code, so constructed was combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction method to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code. In this paper, we provide an improvement by obtaining a much more practical and applicable double error correcting code whose extended version is a triple error correcting code, by combining the same codes as in [1]. Our goal is achieved through using the product code construction approach with the aid of some proven theorems.

How To Cite This Article

@article{Bentse_2018, doi = {10.31559/glm2018.4.3.4}, url = {https://doi.org/10.31559%2Fglm2018.4.3.4}, year = 2018, publisher = {Refaad for Studies and Research}, volume = {4}, number = {3}, pages = {114--119}, author = {CHUN, Pamson Bentse and IBRAHIM Alhaji Aminu and Alhaji Aminu}, title = {A [49 16 6 ]-Linear Code as Product Of The [7 4 2 ] Code Due to Aunu and the Hamming [7 4 3 ] Code}, journal = {General Letters in Mathematics} }
Bentse, C., Pamson, Alhaji Aminu, I., & Aminu, A. (2018). A [49 16 6 ]-Linear Code as Product Of The [7 4 2 ] Code Due to Aunu and the Hamming [7 4 3 ] Code. General Letters in Mathematics, 4(3), 114–119. doi:10.31559/glm2018.4.3.4
[1]C., Pamson Bentse, I. Alhaji Aminu, and A. Aminu, “A [49 16 6 ]-Linear Code as Product Of The [7 4 2 ] Code Due to Aunu and the Hamming [7 4 3 ] Code,” General Letters in Mathematics, vol. 4, no. 3, pp. 114–119, 2018.
Bentse, CHUN, Pamson, IBRAHIM Alhaji Aminu, and Alhaji Aminu. “A [49 16 6 ]-Linear Code as Product Of The [7 4 2 ] Code Due to Aunu and the Hamming [7 4 3 ] Code.” General Letters in Mathematics 4, no. 3 (2018): 114–119. doi:10.31559/glm2018.4.3.4.