Kernel: SageMath 9.5
In [1]:
In [2]:
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In [4]:
cast128_1_00
cast128_1_01
cast128_1_02
cast128_1_03
cast128_1_04
cast128_1_05
cast128_1_06
cast128_1_07
cast128_1_08
cast128_1_09
cast128_1_10
cast128_1_11
cast128_1_12
cast128_1_13
cast128_1_14
cast128_1_15
cast128_1_16
cast128_1_17
cast128_1_18
cast128_1_19
cast128_1_20
cast128_1_21
cast128_1_22
cast128_1_23
cast128_1_24
cast128_1_25
cast128_1_26
cast128_1_27
cast128_1_28
cast128_1_29
cast128_1_30
cast128_1_31
cast128_2_00
cast128_2_01
cast128_2_02
cast128_2_03
cast128_2_04
cast128_2_05
cast128_2_06
cast128_2_07
cast128_2_08
cast128_2_09
cast128_2_10
cast128_2_11
cast128_2_12
cast128_2_13
cast128_2_14
cast128_2_15
cast128_2_16
cast128_2_17
cast128_2_18
cast128_2_19
cast128_2_20
cast128_2_21
cast128_2_22
cast128_2_23
cast128_2_24
cast128_2_25
cast128_2_26
cast128_2_27
cast128_2_28
cast128_2_29
cast128_2_30
cast128_2_31
cast128_3_00
cast128_3_01
cast128_3_02
cast128_3_03
cast128_3_04
cast128_3_05
cast128_3_06
cast128_3_07
cast128_3_08
cast128_3_09
cast128_3_10
cast128_3_11
cast128_3_12
cast128_3_13
cast128_3_14
cast128_3_15
cast128_3_16
cast128_3_17
cast128_3_18
cast128_3_19
cast128_3_20
cast128_3_21
cast128_3_22
cast128_3_23
cast128_3_24
cast128_3_25
cast128_3_26
cast128_3_27
cast128_3_28
cast128_3_29
cast128_3_30
cast128_3_31
cast128_4_00
cast128_4_01
cast128_4_02
cast128_4_03
cast128_4_04
cast128_4_05
cast128_4_06
cast128_4_07
cast128_4_08
cast128_4_09
cast128_4_10
cast128_4_11
cast128_4_12
cast128_4_13
cast128_4_14
cast128_4_15
cast128_4_16
cast128_4_17
cast128_4_18
cast128_4_19
cast128_4_20
cast128_4_21
cast128_4_22
cast128_4_23
cast128_4_24
cast128_4_25
cast128_4_26
cast128_4_27
cast128_4_28
cast128_4_29
cast128_4_30
cast128_4_31
cast128_5_00
cast128_5_01
cast128_5_02
cast128_5_03
cast128_5_04
cast128_5_05
cast128_5_06
cast128_5_07
cast128_5_08
cast128_5_09
cast128_5_10
cast128_5_11
cast128_5_12
cast128_5_13
cast128_5_14
cast128_5_15
cast128_5_16
cast128_5_17
cast128_5_18
cast128_5_19
cast128_5_20
cast128_5_21
cast128_5_22
cast128_5_23
cast128_5_24
cast128_5_25
cast128_5_26
cast128_5_27
cast128_5_28
cast128_5_29
cast128_5_30
cast128_5_31
cast128_6_00
cast128_6_01
cast128_6_02
cast128_6_03
cast128_6_04
cast128_6_05
cast128_6_06
cast128_6_07
cast128_6_08
cast128_6_09
cast128_6_10
cast128_6_11
cast128_6_12
cast128_6_13
cast128_6_14
cast128_6_15
cast128_6_16
cast128_6_17
cast128_6_18
cast128_6_19
cast128_6_20
cast128_6_21
cast128_6_22
cast128_6_23
cast128_6_24
cast128_6_25
cast128_6_26
cast128_6_27
cast128_6_28
cast128_6_29
cast128_6_30
cast128_6_31
cast128_7_00
cast128_7_01
cast128_7_02
cast128_7_03
cast128_7_04
cast128_7_05
cast128_7_06
cast128_7_07
cast128_7_08
cast128_7_09
cast128_7_10
cast128_7_11
cast128_7_12
cast128_7_13
cast128_7_14
cast128_7_15
cast128_7_16
cast128_7_17
cast128_7_18
cast128_7_19
cast128_7_20
cast128_7_21
cast128_7_22
cast128_7_23
cast128_7_24
cast128_7_25
cast128_7_26
cast128_7_27
cast128_7_28
cast128_7_29
cast128_7_30
cast128_7_31
cast128_8_00
cast128_8_01
cast128_8_02
cast128_8_03
cast128_8_04
cast128_8_05
cast128_8_06
cast128_8_07
cast128_8_08
cast128_8_09
cast128_8_10
cast128_8_11
cast128_8_12
cast128_8_13
cast128_8_14
cast128_8_15
cast128_8_16
cast128_8_17
cast128_8_18
cast128_8_19
cast128_8_20
cast128_8_21
cast128_8_22
cast128_8_23
cast128_8_24
cast128_8_25
cast128_8_26
cast128_8_27
cast128_8_28
cast128_8_29
cast128_8_30
cast128_8_31
In [5]:
cast128_2_01:
Algebraic normal form of Boolean function: x0*x1*x2*x6 + x0*x1*x4 + x0*x1*x5 + x0*x1*x6 + x0*x2*x4*x6 + x0*x2*x4 + x0*x2*x5*x6 + x0*x2*x6 + x0*x2 + x0*x3*x5*x6 + x0*x3*x6 + x0*x3 + x0*x4*x6 + x0 + x1*x2*x3*x6 + x1*x2*x4 + x1*x2*x5 + x1*x2*x6 + x1*x3*x4*x6 + x1*x3*x4 + x1*x3*x5 + x1*x3*x6 + x1*x4*x5*x6 + x1*x5*x6 + x1*x5 + x1 + x2*x3*x4*x6 + x2*x3*x4 + x2*x3*x5*x6 + x2*x3*x6 + x2*x4*x5*x6 + x2*x4*x5 + x2*x4*x6 + x2*x4 + x2 + x3*x4*x5*x6 + x3*x4*x5 + x3*x4 + x3*x5 + x4*x5*x6 + x4 + x6*x7
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 8256 extended Cayley classes in the extended translation class.
There are 8256 extended Cayley classes of dual bent functions in the extended translation class,
and 8256 extended Cayley classes in the union of the two.
cast128_2_16:
Algebraic normal form of Boolean function: x0*x1*x2*x3 + x0*x1*x2 + x0*x1*x3*x5 + x0*x1*x3 + x0*x1*x4*x5 + x0*x1*x5*x7 + x0*x1 + x0*x2*x3*x6 + x0*x2*x3*x7 + x0*x2*x3 + x0*x2*x4*x7 + x0*x2*x5*x6 + x0*x2*x5*x7 + x0*x2*x6 + x0*x2*x7 + x0*x2 + x0*x3*x4*x5 + x0*x3*x4*x7 + x0*x3*x4 + x0*x3*x5 + x0*x3*x6 + x0*x3 + x0*x4*x5*x6 + x0*x4*x5*x7 + x0*x5*x7 + x0 + x1*x2*x3*x7 + x1*x2*x3 + x1*x2*x4*x5 + x1*x2*x4*x7 + x1*x2*x4 + x1*x2*x5*x6 + x1*x2*x6 + x1*x3*x4*x7 + x1*x3*x4 + x1*x3*x5*x6 + x1*x3*x5*x7 + x1*x3*x5 + x1*x3*x6 + x1*x3*x7 + x1*x4 + x1*x5*x7 + x1*x5 + x1*x7 + x1 + x2*x3*x4*x7 + x2*x3*x4 + x2*x3*x5*x6 + x2*x3*x5 + x2*x3*x6 + x2*x3*x7 + x2*x4*x5*x7 + x2*x4*x6 + x2*x5*x6 + x2*x5 + x2*x6 + x2*x7 + x2 + x3*x4*x5*x6 + x3*x4*x5 + x3*x4*x6 + x3*x4*x7 + x3*x5*x6 + x3*x6 + x3 + x4 + x6*x7
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 32768 extended Cayley classes in the extended translation class.
There are 32768 extended Cayley classes of dual bent functions in the extended translation class,
and 65536 extended Cayley classes in the union of the two.
cast128_4_27:
Algebraic normal form of Boolean function: x0*x1*x2*x6 + x0*x1*x3 + x0*x1*x5*x6 + x0*x1*x5*x7 + x0*x1*x5 + x0*x1*x6*x7 + x0*x1*x6 + x0*x1*x7 + x0*x2*x3*x7 + x0*x2*x3 + x0*x2*x5*x6 + x0*x2*x5*x7 + x0*x2*x6 + x0*x2 + x0*x3*x4*x6 + x0*x3*x4*x7 + x0*x3*x4 + x0*x3*x5*x6 + x0*x3*x5 + x0*x3*x6*x7 + x0*x3*x6 + x0*x3 + x0*x4*x5*x7 + x0*x4*x6 + x0*x5*x7 + x0*x5 + x0*x6*x7 + x0*x7 + x1*x2*x3*x6 + x1*x2*x3*x7 + x1*x2*x3 + x1*x2*x4*x6 + x1*x2*x6 + x1*x2*x7 + x1*x3*x4*x6 + x1*x3 + x1*x4 + x1*x5*x6 + x1*x5*x7 + x1*x7 + x1 + x2*x3*x4*x6 + x2*x3*x4*x7 + x2*x3*x5*x7 + x2*x4*x5*x6 + x2*x4*x6*x7 + x2*x5*x6*x7 + x2*x5*x6 + x2*x5*x7 + x2*x6*x7 + x3*x5*x6*x7 + x3*x5*x6 + x3*x5*x7 + x3*x5 + x3*x6 + x4*x5*x6*x7 + x4*x5*x6 + x4*x5*x7 + x4*x6*x7 + x4*x6 + x5*x6 + x5*x7 + x5 + x7 + 1
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 65536 extended Cayley classes in the extended translation class.
There are 65536 extended Cayley classes of dual bent functions in the extended translation class,
and 65536 extended Cayley classes in the union of the two.
cast128_5_16:
Algebraic normal form of Boolean function: x0*x1*x2*x6 + x0*x1*x2 + x0*x1*x3*x5 + x0*x1*x3*x6 + x0*x1*x3 + x0*x1*x4*x5 + x0*x1*x4 + x0*x1*x5*x7 + x0*x1*x6 + x0*x2*x3*x5 + x0*x2*x5 + x0*x2*x6 + x0*x2*x7 + x0*x3*x4*x5 + x0*x3*x5 + x0*x3*x6 + x0*x3*x7 + x0*x3 + x0*x4*x5*x6 + x0*x4*x5 + x0*x4*x7 + x0*x5 + x0*x7 + x0 + x1*x2*x3*x6 + x1*x2*x3 + x1*x2*x4 + x1*x2*x5 + x1*x2*x6 + x1*x3*x4*x5 + x1*x3*x5*x7 + x1*x3*x6 + x1*x3 + x1*x5 + x1 + x2*x3*x6 + x2*x3*x7 + x2*x3 + x2*x4*x5*x7 + x2*x4*x6 + x2*x4*x7 + x2*x5*x6 + x2*x5*x7 + x2*x6 + x2 + x3*x4*x5*x6 + x3*x4*x5*x7 + x3*x4*x5 + x3*x4*x6 + x3*x5*x7 + x4*x5*x6 + x4*x5*x7 + x4 + x5*x6 + x5*x7 + x6*x7 + 1
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 33280 extended Cayley classes in the extended translation class.
There are 33280 extended Cayley classes of dual bent functions in the extended translation class,
and 66560 extended Cayley classes in the union of the two.
cast128_5_27:
Algebraic normal form of Boolean function: x0*x1*x2*x7 + x0*x1*x2 + x0*x1*x4*x7 + x0*x1*x5 + x0*x1 + x0*x2*x3*x7 + x0*x2*x3 + x0*x2*x4*x7 + x0*x2*x4 + x0*x2*x7 + x0*x3*x4*x7 + x0*x3*x7 + x0*x3 + x0*x4*x5*x7 + x0*x4*x7 + x0*x5*x7 + x1*x2*x4*x7 + x1*x2*x7 + x1*x2 + x1*x3*x5 + x1*x3*x7 + x1*x3 + x1*x4*x5*x7 + x1*x4*x5 + x1*x4*x7 + x1*x5 + x2*x3*x4*x7 + x2*x3*x4 + x2*x3*x5*x7 + x2*x3*x5 + x2*x3*x7 + x2*x4*x5*x7 + x2*x4*x5 + x2*x4 + x2*x5*x7 + x2*x5 + x3*x4*x5 + x3*x4*x7 + x3*x4 + x3*x5 + x3*x7 + x4 + x6*x7 + x7 + 1
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 6144 extended Cayley classes in the extended translation class.
There are 6144 extended Cayley classes of dual bent functions in the extended translation class,
and 6144 extended Cayley classes in the union of the two.
cast128_6_17:
Algebraic normal form of Boolean function: x0*x1*x3*x7 + x0*x1*x4*x6 + x0*x1*x4 + x0*x1*x5*x6 + x0*x1*x5*x7 + x0*x1*x5 + x0*x1*x6*x7 + x0*x1*x6 + x0*x1 + x0*x2*x3*x6 + x0*x2*x3*x7 + x0*x2*x3 + x0*x2*x4*x6 + x0*x2*x4 + x0*x2*x5*x7 + x0*x2*x6 + x0*x2*x7 + x0*x3*x4*x7 + x0*x3*x5*x6 + x0*x3*x5 + x0*x4*x5*x6 + x0*x4*x5 + x0*x4*x6 + x0*x4*x7 + x0*x4 + x0*x5*x6*x7 + x0*x5*x6 + x0*x6*x7 + x0*x7 + x0 + x1*x2*x3*x6 + x1*x2*x3*x7 + x1*x2*x4*x7 + x1*x2*x4 + x1*x2*x6*x7 + x1*x2*x7 + x1*x2 + x1*x3*x5*x6 + x1*x3*x5*x7 + x1*x3*x6 + x1*x3*x7 + x1*x3 + x1*x4*x5*x6 + x1*x4 + x1*x5*x6*x7 + x1*x5*x6 + x1*x5*x7 + x1*x7 + x2*x3*x4*x7 + x2*x3*x5*x6 + x2*x3*x5 + x2*x3*x7 + x2*x4*x5*x6 + x2*x4*x5 + x2*x4*x6*x7 + x2*x4*x6 + x2*x5*x6*x7 + x2*x5*x6 + x2*x5 + x2*x6 + x2*x7 + x3*x4*x5*x7 + x3*x4*x7 + x3*x5*x6*x7 + x3*x5*x7 + x3*x5 + x3*x6*x7 + x3*x6 + x4*x7 + x4 + x6 + 1
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 65536 extended Cayley classes in the extended translation class.
There are 65536 extended Cayley classes of dual bent functions in the extended translation class,
and 65536 extended Cayley classes in the union of the two.
cast128_7_15:
Algebraic normal form of Boolean function: x0*x1*x2*x4 + x0*x1*x2*x5 + x0*x1*x3*x5 + x0*x1*x3*x6 + x0*x1*x3*x7 + x0*x1*x3 + x0*x1*x4 + x0*x1*x5*x6 + x0*x1*x5*x7 + x0*x1*x5 + x0*x1*x7 + x0*x2*x3*x7 + x0*x2*x3 + x0*x2*x4*x5 + x0*x2*x4*x6 + x0*x2*x4*x7 + x0*x2*x5*x7 + x0*x2*x5 + x0*x2*x6 + x0*x2*x7 + x0*x3*x4*x5 + x0*x3*x4*x6 + x0*x3*x7 + x0*x4*x5*x6 + x0*x4*x5 + x0*x4*x6 + x0*x4*x7 + x0*x4 + x0*x5*x6 + x0*x5 + x0 + x1*x2*x3*x5 + x1*x2*x3*x6 + x1*x2*x3 + x1*x2*x5*x6 + x1*x2*x6 + x1*x2*x7 + x1*x2 + x1*x3*x4 + x1*x3 + x1*x5*x6 + x1*x5*x7 + x1 + x2*x3*x4*x5 + x2*x3*x4*x6 + x2*x4*x5*x6 + x2*x4*x7 + x2*x5*x6 + x2*x5*x7 + x3*x5 + x3 + x4*x5*x7 + x4 + x5*x6 + x5*x7 + x5 + x6*x7
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 32768 extended Cayley classes in the extended translation class.
There are 32768 extended Cayley classes of dual bent functions in the extended translation class,
and 65536 extended Cayley classes in the union of the two.
cast128_7_21:
Algebraic normal form of Boolean function: x0*x1*x2 + x0*x1*x3*x7 + x0*x1*x3 + x0*x1*x4*x7 + x0*x1*x4 + x0*x1*x5*x7 + x0*x1 + x0*x2*x3*x7 + x0*x2*x5*x7 + x0*x2*x5 + x0*x2*x6*x7 + x0*x2*x6 + x0*x3*x4 + x0*x3*x6*x7 + x0*x3*x6 + x0*x3*x7 + x0*x4*x5*x7 + x0*x4*x5 + x0*x4*x6*x7 + x0*x4*x6 + x0*x5*x7 + x0*x6*x7 + x0*x6 + x1*x2*x3*x7 + x1*x2*x3 + x1*x2*x4*x7 + x1*x2*x4 + x1*x2*x5*x6 + x1*x2*x5*x7 + x1*x2 + x1*x3*x4*x6 + x1*x3*x4*x7 + x1*x3*x4 + x1*x3*x5*x7 + x1*x3*x5 + x1*x3*x6*x7 + x1*x3*x7 + x1*x4*x5*x6 + x1*x4*x5*x7 + x1*x4*x6*x7 + x1*x5*x6*x7 + x1*x5*x7 + x1*x6 + x2*x3*x5*x7 + x2*x3*x5 + x2*x3*x7 + x2*x3 + x2*x4*x5*x7 + x2*x4*x5 + x2*x4*x6*x7 + x2*x4*x7 + x2*x5*x6*x7 + x2*x5*x6 + x2*x5*x7 + x2*x5 + x2*x6 + x2*x7 + x2 + x3*x4*x6 + x3*x5*x6*x7 + x3*x6 + x3*x7 + x4*x5*x6*x7 + x4*x5*x6 + x4*x5*x7 + x4*x5 + x4*x6 + x4 + x6 + 1
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 32768 extended Cayley classes in the extended translation class.
There are 32768 extended Cayley classes of dual bent functions in the extended translation class,
and 65536 extended Cayley classes in the union of the two.
In [6]:
Algebraic normal form of Boolean function: x0*x1*x2*x7 + x0*x1*x2 + x0*x1*x4*x7 + x0*x1*x5 + x0*x1 + x0*x2*x3*x7 + x0*x2*x3 + x0*x2*x4*x7 + x0*x2*x4 + x0*x2*x7 + x0*x3*x4*x7 + x0*x3*x7 + x0*x3 + x0*x4*x5*x7 + x0*x4*x7 + x0*x5*x7 + x1*x2*x4*x7 + x1*x2*x7 + x1*x2 + x1*x3*x5 + x1*x3*x7 + x1*x3 + x1*x4*x5*x7 + x1*x4*x5 + x1*x4*x7 + x1*x5 + x2*x3*x4*x7 + x2*x3*x4 + x2*x3*x5*x7 + x2*x3*x5 + x2*x3*x7 + x2*x4*x5*x7 + x2*x4*x5 + x2*x4 + x2*x5*x7 + x2*x5 + x3*x4*x5 + x3*x4*x7 + x3*x4 + x3*x5 + x3*x7 + x4 + x6*x7 + x7 + 1
Function is bent.
SDP design incidence structure t-design parameters: (True, (2, 256, 120, 56))
Classification of Cayley graphs and classification of Cayley graphs of duals differ in matrices of indexes:
There are 6144 extended Cayley classes in the extended translation class.
There are 6144 extended Cayley classes of dual bent functions in the extended translation class,
and 6144 extended Cayley classes in the union of the two.
In [7]:
2023-01-18 02:09:51.627819 before
2023-01-18 02:09:51.794999 after
32914496
In [8]:
2023-01-18 02:09:51.842679 before
2023-01-18 02:09:51.937220 after
32914496
In [9]: