THE PROGRAM

The program is called cmcssac (Central Moment Calculator for Sum of Squares of AutoCorrelation). The specific usage for cmcssac is

./cmcssac [c/m] power_of_central_moment

The first argument is a 'c' (if we only want to count the number of isomorphism classes of contributory partitions) or 'm' (if we want to compute the quasipolynomial formula for the central moment).

The second argument is the positive integer p when we want the pth central moment.

The program presented here (and the data files it generates described in "THE DATA FILES" below) is not the one originally used in preparing the paper.  The program here uses arbitrary precision arithmetic for a larger portion of the calculations, so that fewer of the routines are subject to overflow errors, and some portions were rewritten to conserve memory.  Also the presentation of the output of this version is more polished.  But the program runs somewhat slower than the original.

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THE DATA FILES

For P from 1 to 5, the data file cmcssac-m-P.txt has the data for the Pth central moment.  For P from 1 to 6, there is also a data file cmcssac-c-P.txt, which counts how many isomorphism classes of contributory partitions there are in the calculation of the Pth central moment (but this file does not have a computation of the moment itself).

Each data file starts with the name of the program, a verbatim copy of what was typed on the command line to invoke the program that produced the data being perused, the start time of the run, and a brief description of what the program is attempting to do.

The program first finds representatives of isomorphism classes of contributory partitions via Procedure 5.13 in the paper.  The data gives the count of the number of classes of absolute matrices modulo the equivalence relation in Step (1) of Procedure 5.13.  If the program is in mode "m" (compute moments), it also prints out one absolute matrix per class.  Then the program gives the count of the number of isomorphism classes of contributory partitions.  If the program is in mode "m" (compute moments), it also prints out one monochrome matrix per class that corresponds to that class: these are all the monochrome matrices obtained in Step (2) of Procedure 5.13.  If the program is in mode "m", then after the monochrome matrix we print the size of the isomorphism class (the number of contributory partitions in that class) and we print the quasipolynomial formula for Sols(I,x) where I is the isomorphism class of contributory partitions corresponding to that monochrome matrix and x is the variable that represents the length of the binary sequences.  We print a quasipolynomial function f(x) of period M by printing out M different polynomials, one for each congruence class mod M.  The polynomial that gives the value of f(x) when x is R modulo M is written after the label "R mod M:".  Note that we print a quasipolynomial f(x) with rational coefficients as a product (1/N)*g(x), where N is the least common denominator of all coefficients of all polynomials that make up f(x), and g(x) is a quasipolynomial with integer coefficients.  If we are in mode "m", we then print the overall counting quasipolynomial c(x), that is the quasipolynomial function of x that gives the Pth central moment of sum of squares of autocorrelation for the ensemble of 2^x binary sequences of length x.  If we are in mode "m", we then print the overall counting quasipolynomial c(x) in filtered form, which means that we express it as a sum c(x)=c_0(x)+c_1(x)+...+c_d(x), where c_j(x) is a quasipolynomial where all the constituent polynomial functions are of the form constant*x^j, and we call this c_j(x) the "degree j component" of c(x).  If we are mode "m", we then print LaTeX-friendly tables that list the coefficients of the various c_j(x)'s in a compact form.  By compact form, we mean that if c_j(x) has period M and there are R_1,...,R_t such that the constituent polynomials for c_j(x) when we have x=R_1 (mod M), x=R_2 (mod M), ..., or x=R_t (mod M) all equal the same monomial coeff*x^j, then the table lists R_1,...,R_t in the left-hand column and coeff in the right-hand column.  If we are in mode "m", the data file then has a list, where each line on the list is "cmom P x V", where "cmom" stands for "central moment" P is a positive integer that indicates that we mean the Pth central moment, x is a nonnegative integer that indicates the length of the binary sequences, and V is the Pth central moment of the sum of squares of autocorrelation for the ensemble of 2^x binary sequences of length x.  This last part of the program is useful if we want to check the moments against another program (which should be designed to produce output with the same format).  Finally, the data file records the end time for the run and the duration (in wall clock time to the nearest second and in processor time).