Cayley graphs of binary bent functions of dimension 6.
Import the required modules.
Connect to the database that contains the classifications of bent functions in 6 dimensions.
Create a list c
for the classifications.
Set c
to be the list of classifications for dimension 6, starting from 1, by retrieving these by name. 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[1]
.
Produce a report on the classification c[1]
.
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 algebraic normal form of the bent function corresponding to c[2]
.
Produce a report on the classification c[2]
.
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 algebraic normal form of the bent function corresponding to c[3]
.
Produce a report on the classification c[3]
.
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 algebraic normal form of the bent function corresponding to c[4]
.
Produce a report on the classification c[4]
.
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.
Now use an SQL query on the database to determine which extended Cayley classes are repeated between extended translation classes.
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).
Close the connection to the database, as we no longer need it.
Now take a look at binary projective two weight codes relevant to dimension 6. References: Tonchev 1996, Tonchev 2006.