Modifications on Character Sequences and Construction of Large Even Length Binary Sequences

TL;DR

This paper introduces new modifications to character sequences at composite lengths and constructs large binary sequences of even length with an asymptotic merit factor of 6.0, expanding the known sequence classes with high merit factors.

Contribution

It presents a novel modification method for character sequences at composite lengths and constructs large even-length binary sequences with optimal merit factors.

Findings

Sequences with asymptotic merit factor ≥ 6 are modifications of real primitive characters.

Constructed binary sequences of length 2N with merit factor exactly 6.0.

New sequence modifications enable larger sequences with high merit factors.

Abstract

It has been noticed that all the known binary sequences having the asymptotic merit factor $\ge 6$ are the modifications to the real primitive characters. In this paper, we give a new modification of the character sequences at length $N=p_1p_2\dots p_r$, where $p_i$'s are distinct odd primes and $r$ is finite. Based on these new modifications, for $N=p_1p_2\dots p_r$ with $p_i$'s distinct odd primes, we can construct a binary sequence of length $2N$ with asymptotic merit factor $6.0$