New Extremal Type II Codes Over Z_4
Designs, Codes and Cryptography
Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices
Journal of Algebraic Combinatorics: An International Journal
On type IV self-dual codes over Z4
Discrete Mathematics
Construction of Extremal Type II Codes over \mbox{\zZ}_4
Designs, Codes and Cryptography
A Criterion for Designs in {\tf="P101461" Z}_4-codes on the Symmetrized Weight Enumerator
Designs, Codes and Cryptography
Register Synthesis for Algebraic Feedback Shift Registers Based on Non-Primes
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
Symmetric (4, 4)-nets and generalized Hadamard matrices over groups of order 4
Designs, Codes and Cryptography
On some self-dual codes and unimodular lattices in dimension 48
European Journal of Combinatorics
Construction of MDS self-dual codes over Galois rings
Designs, Codes and Cryptography
Construction of self-dual codes over finite rings Zpm
Journal of Combinatorial Theory Series A
Notes: Extremal Type II Z4-codes of lengths 56 and 64
Journal of Combinatorial Theory Series A
An upper bound on the minimum weight of Type II Z2k-codes
Journal of Combinatorial Theory Series A
The codes and the lattices of Hadamard matrices
European Journal of Combinatorics
Finite Fields and Their Applications
Bounds for Self-Dual Codes Over Z4
Finite Fields and Their Applications
Finite Fields and Their Applications
Classification of Type IV Self-Dual Z4-Codes of Length 16
Finite Fields and Their Applications
On the classification and enumeration of self-dual codes
Finite Fields and Their Applications
Finite Fields and Their Applications
Finite Fields and Their Applications
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Type II Z4-codes are introduced as self-dual codes over the integers modulo 4 containing the all-one vector and with Euclidean weights multiple of 8. Their weight enumerators are characterized by means of invariant theory. A notion of extremality for the Euclidean weight is introduced. Their binary images under the Gray map are formally self-dual with even weights. Extended quadratic residue Z4-codes are the main example of this family of codes. They are obtained by Hensel lifting of the classical binary quadratic residue codes. Their binary images have good parameters. With every type II Z4-code is associated via construction A modulo 4 an even unimodular lattice (type II lattice). In dimension 32, we construct two unimodular lattices of norm 4 with an automorphism of order 31. One of them is the Barnes-Wall lattice BW32