Isodual Codes over {\bb Z}_{2k} and Isodual Lattices
Journal of Algebraic Combinatorics: An International Journal
The Invariants of the Clifford Groups
Designs, Codes and Cryptography
Ternary Code Construction of Unimodular Lattices and Self-Dual Codes over \Bbb Z6
Journal of Algebraic Combinatorics: An International Journal
Orthogonal Designs and Type II Codes over \Bbb{Z}_{2k}
Designs, Codes and Cryptography
Z6-code constructions of the Leech lattice and the Niemeier lattices
European Journal of Combinatorics
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
Jacobi forms over totally real fields and type II codes over Galois rings GR(2m, f)
European Journal of Combinatorics - Special issue on arithmétique et combinatoire
Type II Codes over$$\mathbb{Z}/2k\mathbb{Z}$$, Invariant Rings and Theta Series
Designs, Codes and Cryptography
On some self-dual codes and unimodular lattices in dimension 48
European Journal of Combinatorics
Codes over F4 , Jacobi forms and Hilbert-Siegel modular forms over Q(√5)
European Journal of Combinatorics
On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots
Designs, Codes and Cryptography
Self-dual codes over $$\mathbb{Z}_8$$ and $$\mathbb{Z}_9$$
Designs, Codes and Cryptography
Construction of MDS self-dual codes over Galois rings
Designs, Codes and Cryptography
Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
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
Finite Fields and Their Applications
Finite Fields and Their Applications
On the Hamming Weight Enumerators of Self-Dual Codes over Zk
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 the ring Z2k of the integers modulo 2k with relationships to even unimodular lattices, modular forms, and invariant rings of finite groups. We introduce Type II codes over Z2k which are closely related to even unimodular lattices, as a remarkable class of self-dual codes and a generalization of binary Type II codes. A construction of even unimodular lattices is given using Type II codes. Several examples of Type II codes are given, in particular the first extremal Type II code over Z6 of length 24 is constructed, which gives a new construction of the Leech lattice. The complete and symmetrized weight enumerators in genus g of codes over Z2k are introduced, and the MacWilliams identities for these weight enumerators are given. We investigate the groups which fix these weight enumerators of Type II codes over Z2k and we give the Molien series of the invariant rings of the groups for small cases. We show that modular forms are constructed from complete and symmetrized weight enumerators of Type II codes. Shadow codes over Z2k are also introduced