✦ LIBER ✦
Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem
✍ Scribed by Marcus Greferath
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 106 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
✦ Synopsis
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 Control 37, 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.