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 
Hadamard 
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 
Hadamard 
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 
Hadamard 
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 
Hadamard 
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 
Hadamard 
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 
Hadamard 
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 
Hadamard 
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 
Hadamard 
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 
Hadamard 
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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