Self-dual codes over $$\mathbb{Z}_8$$ and $$\mathbb{Z}_9$$

Authors:
Steven T. Dougherty;T. Aaron Gulliver;John Wong
Affiliations:
Department of Mathematics, University of Scranton, Scranton, USA 18510;Department of Electrical and Computer Engineering, University of Victoria, Victoria, Canada V8W 3P6;Department of Electrical and Computer Engineering, University of Victoria, Victoria, Canada V8W 3P6
Venue:
Designs, Codes and Cryptography
Year:
2006

Citing 4
Cited 5

Shadow lattices and shadow codes

Discrete Mathematics
Handbook of Coding Theory

Handbook of Coding Theory
Type II codes, even unimodular lattices, and invariant rings

IEEE Transactions on Information Theory
On modular cyclic codes

Finite Fields and Their Applications

Construction of MDS self-dual codes over Galois rings

Designs, Codes and Cryptography
The number of self-dual codes over $${Z_{p^3}}$$

Designs, Codes and Cryptography
Mass Formula for Even Codes over

Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
On the Classification of Self-dual -Codes

Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
On self-dual cyclic codes over finite chain rings

Designs, Codes and Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study self-dual codes over the rings $$\mathbb{Z}_8$$ and $$\mathbb{Z}_9$$ . We define various weights and weight enumerators over these rings and describe the groups of invariants for each weight enumerator over the rings. We examine the torsion codes over these rings to describe the structure of self-dual codes. Finally we classify self-dual codes of small lengths over $$\mathbb{Z}_8$$ .