Completely regular codes by concatenating Hamming codes

Joaquim Borges; Josep Rifà; Victor Zinoviev

doi:10.3934/amc.2018021

Article Contents

2018, Volume 12, Issue 2: 337-349. Doi: 10.3934/amc.2018021

This issue Previous Article Locally recoverable codes with availability t≥2 from fiber products of curves Next Article Further results on the existence of super-simple pairwise balanced designs with block sizes 3 and 4

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: May 2018

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).

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Abstract

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.

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Mathematics Subject Classification: Primary: 94B25; Secondary: 94B60.

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References

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