cdn_ehlich {HadamardR}

cdn_ehlich

Description

Checks Hadamard Matrix can be constructed using Ehlich's method.

Usage

cdn_ehlich(order)

Arguments

order

integer

Details

Ehlich (1965)'s construction method requires order of the Hadamard matrix must be a of the form (n-1)^2. Conditions are (i)Order=(n-1)^2; (ii) n is a prime or prime power and 3(mod 4). (iii) (n-2) must be a prime or prime power. In case, if all the three conditions are satisfied, function will return 4 or NULL.

Value

4 or NULL

References

Ehlich, H. (1965). Neue Hadamard-matrizen. Arch. Math., 16, 34-36.

See Also

had_ehlich for Ehlich's construction method.

Examples

cdn_ehlich(36)
#Condition 1:(n-1)^2 = 36 = 6^2
#Condition 2: n=7 (prime)and n=3(mod 4)
#Condition 3: n-2=5 (prime)
#Return
#4
cdn_ehlich(64)
#Condition 1:(n-1)^2 = 64 = 8^2
#Condition 2: n=9 (prime power) but n=1(mod 4).
#Condition 2 fails
#Return
#NULL