Quartic Duadic Sequence Pairs Tending to Infinite Crosscorrelation Merit Factor
Before rotating or adjusting length, we start with a pair of base 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 instances of primes of the form 1+b*b for even integers b.
(So 5 is instance 1, 17 is instance 2, and so forth.)
We check from instance 1 to instance 100, inclusive
For instance N, we use a fractional length as close as possible to N times 0.100000
(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)
Rotation to our base sequences is done first, then length is truncated or periodically extended (appended)
Manifest of Outputs:
This summary file: infinite-cross-merit-1-to-100-summary.txt
Demerit Factors vs. Prime and Fractional Length: infinite-cross-merit-1-to-100-survey.txt
First Column: Underlying Prime p
Second Column: Actual Fractional Length (actual length/p)
Third Column: Actual Fractional Rotation (actual rotation/p)
Fourth Column: Autocorrelation Demerit Factor of First Sequence
Fifth Column: Autocorrelation Demerit Factor of Second Sequence
Sixth Colum: Crosscorrelation Demerit Factor of Sequence Pair