Symmetric \((4,4)\)-nets and generalized Hadamard matrices over groups of order 4

DOI10.1007/s10623-003-4195-yzbMath1055.05019OpenAlexW2085688367MaRDI QIDQ1766098

Masaaki Harada, Vladimir D. Tonchev, Clement Wing Hong Lam

Publication date: 28 February 2005

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-003-4195-y

zbMATH Keywords

error-correcting codesquantum codeHamada conjecturegeneralized Hadamard matrixaffine design

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Other types of codes (94B60) Combinatorial codes (94B25) Finite partial geometries (general), nets, partial spreads (51E14)

Related Items (15)

Linearly embeddable designs ⋮ Extension sets, affine designs, and Hamada's conjecture ⋮ Classification of difference matrices over cyclic groups ⋮ Recent results on designs with classical parameters ⋮ A Hamada type characterization of the classical geometric designs ⋮ New invariants for incidence structures ⋮ Cyclic quasi-symmetric designs and self-orthogonal codes of length 63 ⋮ Line spreads of PG(5, 2) ⋮ Enumeration of generalized Hadamard matrices of order 16 and related designs ⋮ Polarities, quasi-symmetric designs, and Hamada's conjecture ⋮ Hadamard 2-(63,31,15) designs invariant under the dihedral group of order 10 ⋮ Orderly generation of Butson Hadamard matrices ⋮ Generalized weighing matrices and self-orthogonal codes ⋮ On generalized Hadamard matrices of minimum rank ⋮ Kochen-Specker sets and Hadamard matrices

Cites Work

• The number of designs with classical parameters grows exponentially
• Quasi-symmetric \(2\text{-}(31,7,7)\) designs and a revision of Hamada's conjecture
• On projective and affine hyperplanes
• The binary self-dual codes of length up to 32: A revised enumeration
• On the BIB design having the minimum p-rank
• Translations and parallel classes of lines in affine designs
• Classification of affine resolvable \(2\)-\((27,9,4)\) designs
• Shadow codes over \({\mathbb Z}_4\)
• Bounds on the number of affine, symmetric, and Hadamard designs and matrices
• Linear perfect codes and a characterization of the classical designs
• On symmetric nets and generalized Hadamard matrices from affine designs
• Type II codes over Z/sub 4/
• All self-dual Z/sub 4/ codes of length 15 or less are known
• Quantum error correction via codes over GF(4)

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