A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span

TL;DR

This paper introduces a new family of binary sequences with optimal correlation and large linear span, encompassing known sequences as special cases, and provides explicit bounds demonstrating their superior linear span properties.

Contribution

It presents a new sequence family with optimal correlation and larger linear spans than existing sequences, including explicit bounds and special case inclusions.

Findings

Sequences have optimal correlation properties.

Linear span is exponentially larger than existing sequences.

Constructs a class of ideal autocorrelation sequences with large linear span.

Abstract

A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound expression on the linear span of sequences in the family is given. With suitable choices of parameters, it is proved that the family has exponentially larger linear spans than both No sequences and TN sequences. A class of ideal autocorrelation sequences is also constructed and proved to have large linear span.