A Galois Connection Approach to Wei-Type Duality Theorems

In 1991, Wei proved a duality theorem that established an interesting connection between the generalized Hamming weights of linear code and those its dual code. Wei’s has since been extensively studied from different perspectives extended to other settings. this paper, we re-examine various extensions, henceforth referred as Wei-type theorems, new Galois perspective. Our approach is based on observation dimension/length profiles form connection. The central result paper general for two connections finite subsets $\mathbb {Z}$ , which all known theorems can be recovered. As corollaries our result, prove notation="LaTeX">$w$ -demi-matroids defined over sets -demi-polymatroids modules with composition series, further allows us unify generalize codes endowed metrics.