On a question of Babadi and Tarokh II

TL;DR

This paper investigates the randomness properties of Gold sequences, proving that the product of pseudorandom matrices from certain linear codes exhibits randomness in spectral distribution under specific conditions.

Contribution

It improves previous results by establishing the spectral randomness of matrix products from linear codes with dual distance at least 5, answering an open question.

Findings

Spectral distribution of matrix products is random under given conditions.

Dual distance of codes is crucial for spectral randomness.

Provides an affirmative answer to Babadi and Tarokh's question.

Abstract

In this paper we continue to study a question proposed by Babadi and Tarokh \cite{ba2} on the mysterious randomness of Gold sequences. Upon improving their result, we establish the randomness of product of pseudorandom matrices formed from two linear block codes with respect to the empirical spectral distribution, if the dual distance of both codes is at least 5, hence providing an affirmative answer to the question.