# American Institute of Mathematical Sciences

May  2018, 12(2): 337-349. doi: 10.3934/amc.2018021

## Completely regular codes by concatenating Hamming codes

 1 Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Spain 2 A.A. Kharkevich Institute for Problems of Information Transmission, Russian Academy of Sciences, Russia

Received  March 2017 Revised  July 2017 Published  March 2018

Fund Project: This work has been partially supported by the Spanish grants TIN2016-77918-P, AEI/FEDER, UE., MTM2015-69138-REDT; and also by Russian Foundation for Sciences (14-50-00150).

We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of these codes. As a result, we find some non-equivalent completely regular codes, over the same finite field, with the same parameters and intersection array. We also study when the extension of these codes gives completely regular codes. Some of these new codes are completely transitive.

Citation: Joaquim Borges, Josep Rifà, Victor Zinoviev. Completely regular codes by concatenating Hamming codes. Advances in Mathematics of Communications, 2018, 12 (2) : 337-349. doi: 10.3934/amc.2018021
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##### References:
 [1] Agnaldo José Ferrari, Tatiana Miguel Rodrigues de Souza. Rotated $A_n$-lattice codes of full diversity. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020118 [2] Evan Greif, Daniel Kaplan, Robert S. Strichartz, Samuel C. Wiese. Spectrum of the Laplacian on regular polyhedra. Communications on Pure & Applied Analysis, 2021, 20 (1) : 193-214. doi: 10.3934/cpaa.2020263

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