Hadamard designs

Jennifer Wallis

doi:10.1017/s0004972700041599

Hadamard designs

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700041599 ◽

1970 ◽

Vol 2 (1) ◽

pp. 45-54 ◽

Cited By ~ 5

Author(s):

Jennifer Wallis

Keyword(s):

Hadamard Design ◽

Hadamard Designs

In this paper it is shown that an Hadamard design with each letter repeated once and only once can exist for 2, 4 and 8 letters only.L.D. Baumert and Marshall Hall, Jr have found a design with four letters each repeated three times. Their design and the design on four letters each repeated once, found by J. Williamson, is the totality previously published.

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New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830919500575 ◽

2019 ◽

Vol 11 (05) ◽

pp. 1950057

Author(s):

Sara Ban ◽

Dean Crnković ◽

Matteo Mravić ◽

Sanja Rukavina

Keyword(s):

Incidence Matrix ◽

Linear Codes ◽

Minimum Weight ◽

Hadamard Matrices ◽

Binary Codes ◽

Type Ii ◽

Hadamard Design ◽

Binary Linear Codes ◽

Type Formula ◽

Hadamard Designs

For every Hadamard design with parameters [Formula: see text]-[Formula: see text] having a skew-symmetric incidence matrix we give a construction of 54 Hadamard designs with parameters [Formula: see text]-[Formula: see text]. Moreover, for the case [Formula: see text] we construct doubly-even self-orthogonal binary linear codes from the corresponding Hadamard matrices of order 32. From these binary codes we construct five new extremal Type II [Formula: see text]-codes of length 32. The constructed codes are the first examples of extremal Type II [Formula: see text]-codes of length 32 and type [Formula: see text], [Formula: see text], whose residue codes have minimum weight 8. Further, correcting the results from the literature we construct 5147 extremal Type II [Formula: see text]-codes of length 32 and type [Formula: see text].

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