Relative generalized Hamming weights of evaluation codes

The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the next-to-minimal weight of toric codes over hypersimplices of de...

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Veröffentlicht in:	arXiv.org 2021-12
Hauptverfasser:	Jaramillo-Velez, Delio, López, Hiram H, Pitones, Yuriko
Format:	Artikel
Sprache:	eng
Schlagworte:	Computer Science - Information Theory Lower bounds Mathematics - Commutative Algebra Mathematics - Information Theory
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Zusammenfassung:	The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the next-to-minimal weight of toric codes over hypersimplices of degree 1.
ISSN:	2331-8422
DOI:	10.48550/arxiv.2112.07085