Secure CDMA Sequences

TL;DR

This paper introduces a novel method for constructing CDMA sequence sets with high linear complexity, comparable to Legendre sequences, which are verified for very large lengths and have applications in watermarking.

Contribution

A new construction method for CDMA sequences with high linear complexity, including array formats and a reverse process, extending known sequence families.

Findings

Sequences have high linear complexity verified up to length 6x10^8.

Constructed sequences outperform known families in complexity.

New frequency hop patterns with low correlation are introduced.

Abstract

Single sequences like Legendre have high linear complexity. Known CDMA families of sequences all have low complexities. We present a new method of constructing CDMA sequence sets with the complexity of the Legendre from new frequency hop patterns, and compare them with known sequences. These are the first families whose normalized linear complexities do not asymptote to 0, verified for lengths up to 6x108. The new constructions in array format are also useful in watermarking images. We present a conjecture regarding the recursion polynomials. We also have a method to reverse the process, and from small Kasami/No-Kumar sequences we obtain a new family of 2n doubly periodic (2n+1)x(2n-1) frequency hop patterns with correlation 2.