Abstract
MacWilliams' equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in order to make it work in the context of linear codes over finite Frobenius rings.
| Original language | Undefined/Unknown |
|---|---|
| Pages (from-to) | 323-331 |
| Number of pages | 9 |
| Journal | Finite Fields and Their Applications |
| Volume | 8 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2002 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- linear codes over rings
- Frobenius rings
- MacWilliams' equivalence theorem
- homogeneous weights
- Möbius inversion on posets