<s>
In	O
mathematics	O
a	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrix	I-Algorithm
is	O
a	O
Hadamard	O
matrix	O
whose	O
row	O
and	O
column	O
sums	O
are	O
all	O
equal	O
.	O
</s>
<s>
While	O
the	O
order	O
of	O
a	O
Hadamard	O
matrix	O
must	O
be	O
1	O
,	O
2	O
,	O
or	O
a	O
multiple	O
of	O
4	O
,	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrices	I-Algorithm
carry	O
the	O
further	O
restriction	O
that	O
the	O
order	O
be	O
a	O
square	O
number	O
.	O
</s>
<s>
If	O
n	O
=	O
4u2	O
is	O
the	O
order	O
of	O
a	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrix	I-Algorithm
,	O
then	O
the	O
excess	O
is	O
±8u3	O
and	O
the	O
row	O
and	O
column	O
sums	O
all	O
equal	O
±2u	O
.	O
</s>
<s>
If	O
H	O
is	O
interpreted	O
as	O
the	O
incidence	B-Algorithm
matrix	I-Algorithm
of	O
a	O
block	O
design	O
,	O
with	O
1	O
representing	O
incidence	O
and	O
−1	O
representing	O
non-incidence	O
,	O
then	O
H	O
corresponds	O
to	O
a	O
symmetric	O
2-(v,k,λ )	O
design	O
with	O
parameters	O
(	O
4u2	O
,	O
2u2±u	O
,	O
u2±u	O
)	O
.	O
</s>
<s>
A	O
design	O
with	O
these	O
parameters	O
is	O
called	O
a	O
Menon	B-Algorithm
design	I-Algorithm
.	O
</s>
<s>
A	O
number	O
of	O
methods	O
for	O
constructing	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrices	I-Algorithm
are	O
known	O
,	O
and	O
some	O
exhaustive	O
computer	O
searches	O
have	O
been	O
done	O
for	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrices	I-Algorithm
with	O
specified	O
symmetry	O
groups	O
,	O
but	O
it	O
is	O
not	O
known	O
whether	O
every	O
even	O
perfect	O
square	O
is	O
the	O
order	O
of	O
a	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Bush-type	O
Hadamard	O
matrices	O
are	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrices	I-Algorithm
of	O
a	O
special	O
form	O
,	O
and	O
are	O
connected	O
with	O
finite	O
projective	O
planes	O
.	O
</s>
<s>
Like	O
Hadamard	O
matrices	O
more	O
generally	O
,	O
regular	B-Algorithm
Hadamard	I-Algorithm
matrices	I-Algorithm
are	O
named	O
after	O
Jacques	O
Hadamard	O
.	O
</s>
<s>
Menon	B-Algorithm
designs	I-Algorithm
are	O
named	O
after	O
P	O
Kesava	O
Menon	O
,	O
and	O
Bush-type	O
Hadamard	O
matrices	O
are	O
named	O
after	O
Kenneth	O
A	O
.	O
Bush	O
.	O
</s>
