THE PROGRAMS
1. quartic-prime-survey: This is a program for calculating the autocorrelation and crosscorrelation demerit factors of the sequence pairs derived from linear combinations of quartic characters described in the paper in relation to Figures 1 and 2. The usage is
quartic-prime-survey min_prime max_prime trunc_app_ratio filename_stem
min_prime and max_prime specify the range of values for the primes (which are all primes congruent to 1 modulo 4 in the specified range) that are the orders of the fields for which these sequences will be calculated
trunc_app_ratio is the truncation/appending ratio: a positive floating point number that indicates what fraction of a full period p is to be used (so 1.0 means natural length), and if the user specifies a number that is not an exact integer multiple of 1/p, then the program will round to the nearest integer.
filename_stem is the base name for the two output files, which will be named
filename_stem-summary.txt (gives a summary account of the calculation)
filename_stem-survey.txt (first column is the prime, second column is the autocorrelation demerit factor of the first sequence, third column is the autocorrelation demerit factor of the second sequence, fourth column is their crosscorrelation demerit factor)
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2. leg-quartic-prime-survey: This is a program for calculating the autocorrelation and crosscorrelation demerit factors of the sequence pairs derived from linear combinations of quartic characters described in the paper in relation to Figures 3 and 4 of the paper. The first sequence in each pair is derived from a linear combination of quartic characters and the second is derived from the quadratic character (a Legendre sequence, unimodularized). The usage is
leg-quartic-prime-survey min_prime max_prime trunc_app_ratio filename_stem
min_prime and max_prime specify the range of values for the primes (which are all primes congruent to 1 modulo 4 in the specified range) that are the orders of the fields for which these sequences will be calculated
trunc_app_ratio is the truncation/appending ratio: a positive floating point number that indicates what fraction of a full period p is to be used (so 1.0 means natural length), and if the user specifies a number that is not an exact integer multiple of 1/p, then the program will round to the nearest integer.
filename_stem is the base name for the two output files, which will be named
filename_stem-summary.txt (gives a summary account of the calculation)
filename_stem-survey.txt (first column is the prime, second column is the autocorrelation demerit factor of sequence derived from a linear combination of quartic characters, third column is the autocorrelation demerit factor of the unimodularized Legendre sequence, fourth column is their crosscorrelation demerit factor)
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3. infinite-cross-merit: This program calculates the crosscorrelation demerit factors of sequence pairs derived from linear combinations of quartic characters described in the paper in relation to Figure 5 of the paper. The usage is
infinite-cross-merit min_prime_index max_prime_index length_step filename_stem
min_prime_index and max_prime_index specify a range of primes of the form 1+b^2 for b an even integer, so that instance 1 is 5, instance 2 is 17, and so forth.
length_step: we use a truncation/appending ratio equal to the instance number of the prime (see min_prime_index and max_prime_index above) times this number. The truncation/appending ratio is a positive floating point number that indicates what fraction of a full period p is to be used (so 1.0 means natural length), and if the user specifies a number that is not an exact integer multiple of 1/p, then the program will round to the nearest integer. The sequences are also both rotated (cyclically shifted) by an amount described in the paper by an amount that depends on their length.
filename_stem is the base name for the two output files, which will be named
filename_stem-summary.txt (gives a summary account of the calculation)
filename_stem-survey.txt (first Column is the prime p, second column is the fractional length=actual length/p---which should be close to the truncation/appending ratio described above under length_step but is not always exactly equal to it due to rounding, third column=actual fractional rotation=actual rotation from natural shift/p, fourth Column: autocorrelation demerit factor of first sequence, fifth column: autocorrelation demerit factor of second sequence, sixth column: crosscorrelation demerit factor of sequence pair)
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THE DATA, ORGANIZED BY FIGURE
Figure 1. The graph is produced using
quart-1-to-2000-nat-survey.txt
whose contents are all described in
quart-1-to-2000-nat-summary.txt
and these files are produced as outputs by running
./quartic-prime-survey 1 2000 1.0 quart-1-to-2000-nat
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Figure 2. The graph is produced using
leg-quart-1-to-2000-nat-survey.txt
whose contents are all described in
leg-quart-1-to-2000-nat-summary.txt
and these files are produced as outputs by running
./leg-quartic-prime-survey 1 2000 1.0 leg-quart-1-to-2000-nat
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Figure 3. The graph is produced using
quart-1-to-2000-app-survey.txt
whose contents are all described in
quart-1-to-2000-app-summary.txt
and these files are produced as outputs by running
./quartic-prime-survey 1 2000 1.057827 quart-1-to-2000-app
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Figure 4. The graph is produced using
leg-quart-1-to-2000-app-survey.txt
whose contents are all described in
leg-quart-1-to-2000-app-summary.txt
and these files are produced as outputs by running
./leg-quartic-prime-survey 1 2000 1.057827 leg-quart-1-to-2000-app
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Figure 5. The graph is produced using
infinite-cross-merit-1-to-100-survey.txt
whose contents are all described in
infinite-cross-merit-1-to-100-summary.txt
and these files are produced as outputs by running
./infinite-cross-merit 1 100 0.1 infinite-cross-merit-1-to-100