Cartesian square-free codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915612011266048 |
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| author | Carvalho, Cícero López, Hiram H. San-José, Rodrigo |
| author_facet | Carvalho, Cícero López, Hiram H. San-José, Rodrigo |
| contents | The generalized Hamming weights (GHWs) of a linear code C extend the concept of minimum distance, which is the minimum cardinality of the support of all one-dimensional subspaces of C, to the minimum cardinality of the support of all r-dimensional subspaces of the code. In this work, we introduce Cartesian square-free codes, which are linear codes generated by evaluating square-free monomials over a Cartesian set. We use commutative algebraic tools, specifically the footprint bound, to provide explicit formulas for some of the GHWs of this family of codes, and we show how we can translate these results to evaluation codes over the projective space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartesian square-free codes Carvalho, Cícero López, Hiram H. San-José, Rodrigo Information Theory 94B05 (Primary) 81P70, 11T71, 14G50 (Secondary) The generalized Hamming weights (GHWs) of a linear code C extend the concept of minimum distance, which is the minimum cardinality of the support of all one-dimensional subspaces of C, to the minimum cardinality of the support of all r-dimensional subspaces of the code. In this work, we introduce Cartesian square-free codes, which are linear codes generated by evaluating square-free monomials over a Cartesian set. We use commutative algebraic tools, specifically the footprint bound, to provide explicit formulas for some of the GHWs of this family of codes, and we show how we can translate these results to evaluation codes over the projective space. |
| title | Cartesian square-free codes |
| topic | Information Theory 94B05 (Primary) 81P70, 11T71, 14G50 (Secondary) |
| url | https://arxiv.org/abs/2511.08304 |