Loading…
The Construction of Regular Hadamard Matrices by Cyclotomic Classes
For every prime power q ≡ 7 m o d 16 , there are ( q ; a , b , c , d )-partitions of GF ( q ), with odd integers a , b , c , and d , where a ≡ ± 1 m o d 8 such that q = a 2 + 2 ( b 2 + c 2 + d 2 ) and d 2 = b 2 + 2 a c + 2 b d . Many results for the existence of 4 - { q 2 ; q ( q - 1 ) 2 ; q ( q -...
Saved in:
| Published in: | Bulletin of the Iranian Mathematical Society 2021-06, Vol.47 (3), p.601-625 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | For every prime power
q
≡
7
m
o
d
16
, there are (
q
;
a
,
b
,
c
,
d
)-partitions of
GF
(
q
), with odd integers
a
,
b
,
c
, and
d
, where
a
≡
±
1
m
o
d
8
such that
q
=
a
2
+
2
(
b
2
+
c
2
+
d
2
)
and
d
2
=
b
2
+
2
a
c
+
2
b
d
. Many results for the existence of
4
-
{
q
2
;
q
(
q
-
1
)
2
;
q
(
q
-
2
)
}
SDS which are simple homogeneous polynomials of parameters
a
,
b
,
c
and
d
of degree at most 2 have been found. Hence, for each value of
q
, the construction of SDS becomes equivalent to building a
(
q
;
a
,
b
,
c
,
d
)
-partition. Once this is done, the verification of the construction only involves verifying simple conditions on
a
,
b
,
c
and
d
which can be done manually. |
|---|---|
| ISSN: | 1017-060X 1735-8515 |
| DOI: | 10.1007/s41980-020-00402-9 |