Relative generalized Hamming weights of evaluation codes

Published 14 Dec 2021 in cs.IT, math.AC, and math.IT | (2112.07085v1)

Abstract: 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.

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