Designs and their codes
Handbook of Coding Theory
Handbook of Coding Theory
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
On the Hamming distance of linear codes over a finite chain ring
IEEE Transactions on Information Theory
On the classification and enumeration of self-dual codes
Finite Fields and Their Applications
Negacyclic self-dual codes over finite chain rings
Designs, Codes and Cryptography
Self-dual codes over commutative Frobenius rings
Finite Fields and Their Applications
On self-dual cyclic codes over finite chain rings
Designs, Codes and Cryptography
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We study self-dual codes over chain rings. We describe a technique for constructing new self-dual codes from existing codes and we prove that for chain rings containing an element c with c² = −1, all self-dual codes can be constructed by this technique. We extend this construction to self-dual codes over principal ideal rings via the Chinese Remainder Theorem. We use torsion codes to describe the structure of self-dual codes over chain rings and to set bounds on their minimum Hamming weight. Interestingly, we find the first examples of MDS self-dual codes of lengths 6 and 8 and near-MDS self-dual codes of length 10 over a certain chain ring which is not a Galois ring.