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# Balanced and constant functions as seen by Hadamard 1 1 1 1 1 -1 1 -1 Notes | EduRev

## : Balanced and constant functions as seen by Hadamard 1 1 1 1 1 -1 1 -1 Notes | EduRev

Page 1

Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
1
1
1
1
=
4
0
0
0
Matrix M
Vector V
Vector S
This is number of
minterms “0” in the
function
This is
measure of
correlation
with other
rows of M
Constant 0
Ones in map
encoded by “-1”,
zeros by “1”
Page 2

Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
1
1
1
1
=
4
0
0
0
Matrix M
Vector V
Vector S
This is number of
minterms “0” in the
function
This is
measure of
correlation
with other
rows of M
Constant 0
Ones in map
encoded by “-1”,
zeros by “1”
Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
-1
-1
-1
-1
=
- 4
0
0
0
Matrix M
Vector V
Vector S
This is number of
minterms “1” in the
function
This is
measure of
correlation
with other
rows of M
Constant 1
Page 3

Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
1
1
1
1
=
4
0
0
0
Matrix M
Vector V
Vector S
This is number of
minterms “0” in the
function
This is
measure of
correlation
with other
rows of M
Constant 0
Ones in map
encoded by “-1”,
zeros by “1”
Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
-1
-1
-1
-1
=
- 4
0
0
0
Matrix M
Vector V
Vector S
This is number of
minterms “1” in the
function
This is
measure of
correlation
with other
rows of M
Constant 1
Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
1
-1
1
-1
=
0
4
0
0
Matrix M
Vector V
Vector S
balanced
This means we
have half “1”
and half “0s”
Page 4

Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
1
1
1
1
=
4
0
0
0
Matrix M
Vector V
Vector S
This is number of
minterms “0” in the
function
This is
measure of
correlation
with other
rows of M
Constant 0
Ones in map
encoded by “-1”,
zeros by “1”
Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
-1
-1
-1
-1
=
- 4
0
0
0
Matrix M
Vector V
Vector S
This is number of
minterms “1” in the
function
This is
measure of
correlation
with other
rows of M
Constant 1
Balanced and constant functions as seen by
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
1
-1
1
-1
=
0
4
0
0
Matrix M
Vector V
Vector S
balanced
This means we
have half “1”
and half “0s”
Local patterns for Affine
functions
1 0 1 0
0 1 0 1
1 0 1 0
0 1 0 1
1 1 0 0
0 0 1 1
1 1 0 0
0 0 1 1
00
01
11
10
00  01  11  10
ab
cd
a ? b ? c ?d ?1
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