Relative generalized Hamming weights of evaluation codes

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.

References in corpus (2)

• Relative generalized Hamming weights of one-point algebraic geometric codes
• The next-to-minimal weights of binary projective Reed-Muller codes