Quartic Duadic Sequence Prime Survey
Before rotating or adjusting length, we start with a pair of binary sequences
The first assigns +1 to powers 4*k,4*k+1 of the primitive element mod p (and -1 to powers 4*k+2,4*k+3)
The second assigns +1 to powers 4*k,4*k+3 of the primitive element mod p (and -1 to powers 4*k+1,4*k+2)
Both sequences unimodularize zero entries to ones.
(The primitive element is always the reduction modulo p of the smallest positive integer that produces a primitive element in this way.)
We are checking the 147 primes that are 1 modulo 4 between 1 and 2000 (inclusive)
that produce a sequene of positive length with Truncating/Appending Ratio near: 1.000000
(we try length prime*desired ratio, and round to the nearest integer (rounding 1/2 up)
Each sequence is rotated by a fractional rotation as close as possible to (3-2*actual fractional length)/4 to optimize autocorrelation.
(we try rotation prime*desired ratio, and round to the nearest integer (rounding 1/2 up)
Manifest of Outputs:
This summary file: quart-1-to-2000-nat-summary.txt
Demerit Factors vs. Prime: quart-1-to-2000-nat-survey.txt
First Column: Underlying Prime p
Second Column: Real Part of G(chi)^4/p^2, where chi is a quartic character modulo p
Third Column: Autocorrelation Demerit Factor of First Sequence
Fourth Column: Autocorrelation Demerit Factor of Second Sequence
Fifth Colum: Crosscorrelation Demerit Factor of Sequence Pair