$m$-Sequences of Different Lengths with Four-Valued Cross Correlation

TL;DR

This paper constructs an infinite family of pairs of m-sequences of different lengths with four-valued cross correlation and determines their complete correlation distribution, advancing understanding of sequence correlation properties.

Contribution

It introduces a new family of m-sequence pairs of different lengths with four-valued cross correlation and fully characterizes their correlation distribution.

Findings

Constructed an infinite family of m-sequence pairs with four-valued cross correlation.

Determined the complete correlation distribution for this family.

Enhanced understanding of cross correlation properties of sequences of different lengths.

Abstract

{\bf Abstract.} Considered is the distribution of the cross correlation between $m$-sequences of length $2^m-1$, where $m$ is even, and $m$-sequences of shorter length $2^{m/2}-1$. The infinite family of pairs of $m$-sequences with four-valued cross correlation is constructed and the complete correlation distribution of this family is determined.