Type II self-dual codes over finite rings and even unimodular lattices

DOI10.1023/A:1018696102510zbMath0958.94037MaRDI QIDQ1301859

Steven T. Dougherty, Masaaki Harada, T. Aaron Gulliver

Publication date: 3 February 2000

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

zbMATH Keywords

double circulant codeeven unimodular latticeself-dual code over finite ringType II code

Mathematics Subject Classification ID

Other types of codes (94B60)

Related Items (22)

Construction of self-dual codes over \(\mathbb {Z}_{2^{m}}\) ⋮ On the ℤ_q-Simplex codes and its weight distribution for dimension 2 ⋮ Construction of extremal self-dual codes over \(\mathbb Z_8\) and \(\mathbb Z_{16}\) ⋮ Type II codes over finite rings ⋮ On ℤ_q-linear and ℤ_q-Simplex codes and its related parameters forqis a prime power ⋮ Cyclic self-orthogonal codes over finite chain ring ⋮ Construction of self-dual codes over finite rings \(\mathbb Z_{p^m}\) ⋮ Construction of extremal type II \(\mathbb{Z}_{2 k}\)-codes ⋮ Mass formulae for Euclidean self-orthogonal and self-dual codes over finite commutative chain rings ⋮ On the covering radius of some modular codes ⋮ On codes over ℤp2 and its covering radius ⋮ Codes over rings and Hermitian lattices ⋮ Constructing self-dual codes over \(\mathbb{F}_q[u/(u^t)\)] ⋮ On cyclic self-orthogonal codes over \(\mathbb{Z}_{2^m}\) ⋮ A note on negacyclic self-dual codes over \(\mathbb Z_{2^{a}}\) ⋮ On the classification and enumeration of self-dual codes ⋮ Construction of MDS self-dual codes over Galois rings ⋮ On covering radius of codes over ℤ2p ⋮ On the Hamming weight enumerators of self-dual codes over \(\mathbb{Z}_k\) ⋮ Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey) ⋮ Extremal double circulant type II codes over \(\mathbb Z_4\) and construction of 5-(24,10,36) designs. ⋮ A method for constructing self-dual codes over \(\mathbb {Z}_{2^m}\)

Cites Work

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• Double circulant codes over \(\mathbb{Z}_ 4\) and even unimodular lattices
• Self-dual doubly circulant codes
• Selbstduale Codes über dem Ring der ganzen Zahlen modulo 4. (Self-dual codes over the ring of integers modulo 4)
• The binary self-dual codes of length up to 32: A revised enumeration
• Self-dual codes over the integers modulo 4
• Cyclic self-dual \(\mathbb Z_4\)-codes.
• New extremal type II codes over \(\mathbb{Z}_4\)
• Modular and \(p\)-adic cyclic codes
• Duality for modules over finite rings and applications to coding theory
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Type II codes over Z/sub 4/
• Quaternary quadratic residue codes and unimodular lattices
• Cyclic codes and quadratic residue codes over Z/sub 4/
• An upper bound for self-dual codes

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