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Blue Waters computing the Tutte Polynomial of ReedMullerCode(2, 6)

Blue Waters is a petascale supercomputer at the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana--Champaign (UIUC). It was the fastest supercomputer at a university anywhere in the world until TACC Frontera came online in 2019.

The [64, 22, 16]-Reed-Muller code, also known as RM(2, 6), is the linear code over GF(2) generated by this matrix (expressed in python syntax):

[
  [ c&r == 0 for c in range(64) ]
             for r in range(64) if bin(r).count('1') < 3
]

More precisely, RM(2, 6) is generated by this matrix:

################################################################
#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-
##--##--##--##--##--##--##--##--##--##--##--##--##--##--##--##--
#---#---#---#---#---#---#---#---#---#---#---#---#---#---#---#---
####----####----####----####----####----####----####----####----
#-#-----#-#-----#-#-----#-#-----#-#-----#-#-----#-#-----#-#-----
##------##------##------##------##------##------##------##------
########--------########--------########--------########--------
#-#-#-#---------#-#-#-#---------#-#-#-#---------#-#-#-#---------
##--##----------##--##----------##--##----------##--##----------
####------------####------------####------------####------------
################----------------################----------------
#-#-#-#-#-#-#-#-----------------#-#-#-#-#-#-#-#-----------------
##--##--##--##------------------##--##--##--##------------------
####----####--------------------####----####--------------------
########------------------------########------------------------
################################--------------------------------
#-#-#-#-#-#-#-#-#-#-#-#-#-#-#-#---------------------------------
##--##--##--##--##--##--##--##----------------------------------
####----####----####----####------------------------------------
########--------########----------------------------------------
################------------------------------------------------

We compute its Tutte--Whitney polynomial and more general invariants on Blue Waters. See the resulting polynomial in matrix form.

See also the Blue Waters Annual Report, page 109.

For the general idea behind the computation, visit process overview and links therein. The full data set (modulo testing and log files etc) is uploaded to my Google Drive .edu account.

One can also challenge the computation: The full computation costs 2,000 node-hours. We deliberately divide the computation into 48,520 subjobs so that anyone can challenge our computation by rerunning only a subset of subjobs. This makes our computation (economically) falsifiable.

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Computation of Reed-Muller codes of length 64 on Blue Waters

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