Finite-ring combinatorics and MacWilliams' equivalence theorem
Journal of Combinatorial Theory Series A
Handbook of Coding Theory
Euclidean and hermitian self-dual MDS codes over large finite fields
Journal of Combinatorial Theory Series A
On the Equivalence of Codes over Finite Rings
Applicable Algebra in Engineering, Communication and Computing
Self-Dual Codes and Invariant Theory (Algorithms and Computation in Mathematics)
Self-Dual Codes and Invariant Theory (Algorithms and Computation in Mathematics)
Construction of MDS self-dual codes over Galois rings
Designs, Codes and Cryptography
MDS codes over finite principal ideal rings
Designs, Codes and Cryptography
Independence of vectors in codes over rings
Designs, Codes and Cryptography
Constructions of self-dual codes over finite commutative chain rings
International Journal of Information and Coding Theory
Weight enumerators of self-dual codes
IEEE Transactions on Information Theory
The Z4-linearity of Kerdock, Preparata, Goethals, and related codes
IEEE Transactions on Information Theory
Shadow codes and weight enumerators
IEEE Transactions on Information Theory
On the equivalence of codes over rings and modules
Finite Fields and Their Applications
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We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We generalize the building-up construction for finite commutative Frobenius rings, showing that all self-dual codes with minimum weight greater than 2 can be obtained in this manner in cases where the construction applies.