CoCalc Public FilesBoolean-Cayley-graphs / sage-code / cayley_graphs_boolean_dimension_2.ipynbOpen with one click!

1

Import the required modules.

2

In [1]:

import os from boolean_cayley_graphs.bent_function import BentFunction from boolean_cayley_graphs.bent_function_cayley_graph_classification import BentFunctionCayleyGraphClassification

3

Connect to the database that contains the classifications of bent functions in 2 dimensions.

4

In [2]:

load("boolean_dimension_cayley_graph_classifications.py")

5

Set `c`

to be the list of classifications for dimension 2, starting from 1. `c[0]`

is `None`

.

6

In [3]:

c = save_boolean_dimension_cayley_graph_classifications(2, dir=os.path.join("..","sobj"))

7

Display the length of c, the list of classifications.

8

In [4]:

len(c)

9

2

Verify that `c[0]`

is `None`

.

10

In [5]:

print(c[0])

11

None

Print the algebraic normal form of the bent function corresponding to `c[1]`

.

12

In [6]:

c[1].algebraic_normal_form

13

x0*x1

Produce a report on the classification `c[1]`

.

14

In [7]:

c[1].report(report_on_graph_details=True)

15

Algebraic normal form of Boolean function: x0*x1
Function is bent.
SDP design incidence structure t-design parameters: (True, (1, 4, 1, 1))
Classification of Cayley graphs and classification of Cayley graphs of duals are the same:
There are 2 extended Cayley classes in the extended translation class.
For each extended Cayley class in the extended translation class:
Clique polynomial, strongly regular parameters, rank, and order of a representative graph; and
linear code and generator matrix for a representative bent function:
EC class 0 :
Algebraic normal form of representative: x0*x1
Clique polynomial: 2*t^2 + 4*t + 1
Strongly regular parameters: (4, 1, 0, 0)
Rank: 4 Order: 8
Linear code from representative:
[1, 1] linear code over GF(2)
Generator matrix:
[1]
Linear code is projective.
Weight distribution: {0: 1, 1: 1}
EC class 1 :
Algebraic normal form of representative: x0*x1 + x0 + x1
Clique polynomial: t^4 + 4*t^3 + 6*t^2 + 4*t + 1
Strongly regular parameters: False
Rank: 4 Order: 24
Linear code from representative:
[3, 2] linear code over GF(2)
Generator matrix:
[1 0 1]
[0 1 1]
Linear code is projective.
Weight distribution: {0: 1, 2: 3}

Produce a matrix plot of the `weight_class_matrix`

.

16

In [8]:

matrix_plot(c[1].weight_class_matrix,cmap='gist_stern')

17

Produce a matrix plot of `bent_cayley_graph_index_matrix`

, the matrix of indices of extended Cayley classes within the extended translation class.

18

In [9]:

matrix_plot(c[1].bent_cayley_graph_index_matrix,cmap='gist_stern')

19

In [ ]:

20