Relative generalized Hamming weights of evaluation codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866917583128625152 |
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| author | Jaramillo-Velez, Delio López, Hiram H. Pitones, Yuriko |
| author_facet | Jaramillo-Velez, Delio López, Hiram H. Pitones, Yuriko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_07085 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Relative generalized Hamming weights of evaluation codes Jaramillo-Velez, Delio López, Hiram H. Pitones, Yuriko Information Theory Commutative Algebra 13P25, 14G50, 94B27, 11T71 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. |
| title | Relative generalized Hamming weights of evaluation codes |
| topic | Information Theory Commutative Algebra 13P25, 14G50, 94B27, 11T71 |
| url | https://arxiv.org/abs/2112.07085 |