Cayley graphs of binary bent functions of dimension 6.
Import the required modules.
Import controls.
Turn on verbose output.
Connect to the database that contains the classifications of bent functions in 6 dimensions.
Set c
to be the list of classifications for dimension 6. c[0]
is None
.
Display the length of c, the list of classifications.
Verify that c[0]
is None
.
Print the algebraic normal form of the bent function corresponding to c[n]
.
Produce a report on the classification c[n]
.
Produce a matrix plot of the weight_class_matrix
.
Produce a matrix plot of bent_cayley_graph_index_matrix
, the matrix of indices of extended Cayley classes within the extended translation class.
Print the number of distinct bent functions within the Extended Translation Class, and produce a matrix plot showing where these occur within the class.
Print the algebraic normal form of the bent function corresponding to c[n]
.
Produce a report on the classification c[n]
.
Produce a matrix plot of the weight_class_matrix
.
Produce a matrix plot of bent_cayley_graph_index_matrix
, the matrix of indices of extended Cayley classes within the extended translation class.
Print the number of distinct bent functions within the Extended Translation Class, and produce a matrix plot showing where these occur within the class.
Print the algebraic normal form of the bent function corresponding to c[n]
.
Produce a report on the classification c[n]
.
Produce a matrix plot of the weight_class_matrix
.
Produce a matrix plot of bent_cayley_graph_index_matrix
, the matrix of indices of extended Cayley classes within the extended translation class.
Print the number of distinct bent functions within the Extended Translation Class, and produce a matrix plot showing where these occur within the class.
Print the algebraic normal form of the bent function corresponding to c[n]
.
Produce a report on the classification c[n]
.
Produce a matrix plot of the weight_class_matrix
.
Produce a matrix plot of bent_cayley_graph_index_matrix
, the matrix of indices of extended Cayley classes within the extended translation class.
Print the number of distinct bent functions within the Extended Translation Class, and produce a matrix plot showing where these occur within the class.
Test to see if the bent functions corresponding to each pair of classifications are general linear equivalent or extended Cayley equivalent
Test to see if the bent functions corresponding to c[1]
and c[2]
are extended Cayley equivalent
Double check that the boolean function corresponding to c[2]
has an extended translation class that contains 15 different general linear equivalence classes.
Now produce a reclassification r
by seeing which extended Cayley classes are repeated between extended translation classes.
Each entry in reclassification_table
has as row 0, the "global" index of each extended Cayley class in the extended translation class.
Row 1 contains the local index of each extended Cayley class in the extended translation class, as given by the corresponding bent functions.
Row 2 contains the size of each extended Cayley class in the extended translation class, as given by the corresponding bent functions.
Row 3 contains the local index of each extended Cayley class in the extended translation class, as given by the Walsh Hadamard dual of each of the corresponding bent functions.
Row 4 contains the size of each extended Cayley class in the extended translation class, as given by the Walsh Hadamard dual of each of the corresponding bent functions.
We see that:
Extended Cayley class 0 occurs in both Extended Translation class 1 (2304 Cayley graphs) and Extended Translation class 2 (512 Cayley graphs).
The list r.classification_list
contains the classifications in c
, but with each of the matrices bent_cayley_graph_index_matrix
and dual_cayley_graph_index_matrix
using the indices from row 0 of reclassification_table
corresponding to each index from row 1 and row 3 respectively.