Enumeration of generalized Hadamard matrices of order 16 and related designs

Gibbons, Peter B.; Mathon, Rudolf

doi:10.1002/jcd.20193

Cited by 8 publications

(10 citation statements)

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“…In [37] Horadam and Farmer also show there are 1446 equivalence classes of central (16,16,16,1)-RDSs relative to Z 4 2 ; this is not a power of 2. Even if RP 53 is restricted to isotopism classes of fields, the number of RDS equivalence classes is not a power of 2, as even though there are 1, 2, 4, 32 bundles over GF (2), GF(4), GF (8), GF (16), respectively, there are 2094 bundles over GF (32).…”

Section: Multiplicative Rdss and Presemif Ields: Rp 50 Rp 53 Rp 74 mentioning

confidence: 97%

Hadamard matrices and their applications: Progress 2007–2010

Horadam

2010

Cryptogr. Commun.

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Section: Multiplicative Rdss and Presemif Ields: Rp 50 Rp 53 Rp 74 mentioning

confidence: 97%

Hadamard matrices and their applications: Progress 2007–2010

Horadam

2010

Cryptogr. Commun.

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“…All nonisomorphic class-regular symmetric (4, 4)-nets were enumerated by Harada, Lam and Tonchev in [4], and, implicitly, by Gibbons and Mathon in [3] (two incidence structures are isomorphic if there is an incidence preserving bijection between their point sets). Up to isomorphism, there are exactly 226 nets with group of bitranslations N = Z 2 × Z 2 , and 13 nets with N = Z 4 .…”

Section: Rds and Symmetric Netsmentioning

confidence: 99%

Enumeration of (16,4,16,4) Relative Difference Sets

Clark

Tonchev

2013

Electron. J. Combin.

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A complete enumeration of relative difference sets (RDS) with parameters $(16,4,16,4)$ in a group of order 64 with a normal subgroup $N$ of order 4 is given. If $N=Z_4$, three of the 11 abelian groups of order 64, and 23 of the 256 nonabelian groups of order 64 contain $(16,4,16,4)$ RDSs. If $N=Z_2 \times Z_2$, nine of the abelian groups and 194 of the non-abelian groups of order 64 contain $(16,4,16,4)$ RDSs.

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“…Of course, meanwhile also all generalized Hadamard matrices of order 16 were classified (cf. [41]). However, for this order too many matrices arise to give each of them a special attention.…”

Section: About Sourcementioning

confidence: 99%

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

Klin

Pech²

2011

Ars Math. Contemp.

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New constructions of regular distance regular antipodal covers (in the sense of GodsilHensel) of complete graphs K n are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n 2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T . Further, a new regular cover of K 45 on 135 vertices is produced with the aid of a decoration of the alternating group A 6 .

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Enumeration of generalized Hadamard matrices of order 16 and related designs

Cited by 8 publications

References 8 publications

Hadamard matrices and their applications: Progress 2007–2010

Hadamard matrices and their applications: Progress 2007–2010

Enumeration of (16,4,16,4) Relative Difference Sets

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

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