1970-01-01

(2026-04) Beyond Binary; crosscorrelation of Quartic and Cubic Character Sequences

• [[Mriganka Dey]]
• [[Sampa Dey]]
• [[Sampurna Pal]]
• [[Subhabrata Samajder]]
• [[Rana Barua]]

2026-04-28

Abstract

The arithmetic crosscorrelation of pseudorandom sequences is a fundamental measure of their suitability for applications in cryptography and communications. While prior works have studied this quantity for binary sequences, the non-binary setting has remained largely open. In this paper, we initiate a systematic study of arithmetic crosscorrelation for non-binary pseudorandom sequences constructed from higher-order multiplicative characters over finite fields. For two quartic sequences of co-prime periods $P$ and $Q$ defined via polynomials of degree $d$, we establish that $\left|C^{A}_{\mathcal{S},\mathcal{T}}(\tau)\right| \ \ll \ dP^{1/2}Q(\log P)^{2},$ for all shifts $\tau$, using character orthogonality, joint pattern distribution and the Weil bound. An analogous bound is also derived for cubic character sequences. To the best of our knowledge, these are the first nontrivial upper bounds on the arithmetic crosscorrelation of non-binary pseudorandom sequences, generalizing prior works of Chen et al. (IEEE IT, 2022) and Yan and Ke (eprint archive, 2026).