Third update on Boolean-Cayley-graphs

[Paul Leopardi]

An update on my previous post.

So far my project to classify bent functions by their Cayley graphs has resulted in the following. 

• The paper "Classifying bent functions by their Cayley graphs", was rejected by INTEGERS: The Electronic Journal of Combinatorial Number Theory. I have since revised it, but have not submitted the revised version (v6) to a journal. Any suggestions for journals are welcome.
  

https://arxiv.org/abs/1705.04507 

• A prototype Bent function - Cayley graph virtual laboratory using a PostgreSQL relational database, hosted by NeCTAR.
  This contains Cayley graph classifications of all of the extended affine equivalence classes of bent functions mentioned in the paper, except for the partial spread bent functions. 
  This acts as a temporary (until June 2019) database of supplementary material for the paper. 
  In particular, the CAST-128 database contains 32 914 496 non-isomorphic stongly regular graphs with parameters (256,120,56,56) or (256,136,72,72), obtained from 63 GB of sobj files.  
  

http://vm-130-56-248-117.nci.org.au/bfcg/

• The Boolean-Cayley-graphs source code repository, including the Python boolean_cayley_graphs package and LaTeX source of all related papers and presentations.
  

https://github.com/penguian/Boolean-Cayley-graphs 

• The boolean-cayley-graphs project on PyPI, a pip installable version of the Python boolean_cayley_graphs package.

https://pypi.org/project/boolean-cayley-graphs/

• Documentation of the Python boolean_cayley_graphs package. Doctest coverage is 100% except for functions that use MPI.
  

https://boolean-cayley-graphs.sourceforge.io/ 

• The Boolean-Cayley-graphs public directory on CoCalc, based on the source code repository
  

https://cocalc.com/projects/80f4c9e7-8a37-4f59-82e7-aa179ec0b652/files/Boolean-Cayley-graphs/

• Cayley graph classifications of all of the 5442 extended affine equivalence classes of partial spread (+) bent functions and the 9316 extended affine equivalence classes of partial spread (-) bent functions in 8 dimensions. 
  This comprises 6.1TB of sobj files. These are stored on the NCI Massdata store attached to Raijin, as well as the /g/data file system, and on two Seagate 6TB Backup Plus Hub removable drives.
  My ambition is to find a way to host a semi-permanent multi-Terabyte public database of bent function Cayley graph classifications, including all 14 758 partial spread bent functions, and up to about 2 billion non-isomorphic strongly regular Cayley graphs. This *might* be hosted by Australian Research Data Commons.
  

Anyone who wants to examine the Sage and Python code is welcome to do so. Please contribute issues via the Boolean-Cayley-graphs Github project. I have many ideas for issues, starting with 

(1) porting to Python 3, and extending through 

(2) a more complete database interface, based on the Sagemath sql_db module, and 

(3) a revision of the modules and classes with respect to Python 3, informed by works such as Fluent Python, and finally

(4) an equivalent Sage package.

I am especially interested in anyone who wants to help with the multi-Terabyte database and hosting effort, and anyone who wants to study the statistics of billions of non-isomorphic strongly regular graphs.