On parameters of subfield subcodes of extended norm-trace codes

Heeralal Janwa; Fernando L. Piñero

doi:10.3934/amc.2017032

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2017, Volume 11, Issue 2: 379-388. Doi: 10.3934/amc.2017032

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On parameters of subfield subcodes of extended norm-trace codes

Heeralal Janwa^1, and
Fernando L. Piñero^2,

1.
Department of Mathematics, Faculty of Natural Sciences, University of Puerto Rico -Río Piedras Campus, San Juan, Puerto Rico, 00925 USA
2.
Department of Mathematics, University of Puerto Rico -Ponce Campus, Ponce, Puerto Rico, 00716 USA

Received: January 31, 2016

Revised: February 29, 2016

Published: September 2017

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Abstract

In this article we describe how to find the parameters of subfield subcodes of extended Norm-Trace codes (ENT codes). With a Gröbner basis of the ideal of the $\mathbb{F}_{q^r}$ rational points of the extended Norm-Trace curve one can determine the dimension of the subfield subcodes or the dimension of the trace code. We also find a BCH-like bound from the minimum distance of the original code. The ENT codes we study here are a more general class of codes than those given in [1]. We study their subfield subcodes as well. We give an example of ENT subfield subcodes that have optimal parameters. Furthermore, we give examples of binary subfield subcodes of ENT codes of very large length for modern applications (e.g. for flash memories).

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Mathematics Subject Classification: Primary: 14G50, 11T71; Secondary: 13P10.

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References

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