Cartesian square-free codes
Abstract
Abstract The generalized Hamming weights (GHWs) of a linear code extend the concept of minimum distance, which is the minimum weight of all one-dimensional subspaces of C , to the minimum weight 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.
Fields of Study & Subjects
Coding theory and cryptography
Error Correcting Code Techniques
graph theory and CDMA systems
Publication details
- Journal / source
- Boletín de la Sociedad Matemática Mexicana
- Volume
- 32
- Issue
- 3
- Publication date
- 1 September 2026
- Language
- EN