Classification of normal sequences

TL;DR

This paper introduces a new equivalence classification for normal sequences, constructs a canonical form, and enumerates all classes for sequence length up to 40, advancing combinatorial sequence analysis.

Contribution

It defines a new equivalence relation for normal sequences and provides a complete enumeration for lengths up to 40.

Findings

Enumerated all equivalence classes of NS(n) for n ≤ 40

Developed a canonical form for normal sequences

Established a new framework for classifying base sequences

Abstract

Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, with A and B of length m and C and D of length n, such that the sum of their nonperiodic autocorrelation functions is a delta-function. Normal sequences NS(n) are base sequences (A;B;C;D) in BS(n,n) such that A=B. We introduce a definition of equivalence for normal sequences NS(n), and construct a canonical form. By using this canonical form, we have enumerated the equivalence classes of NS(n) for n <= 40.