2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude

Abstract

Three constructions of binary sequences with period 4N and optimal autocorrelation value or optimal autocorrelation magnitude have been presented by Tang and Gong based on interleaving technique. In this paper, the 2-adic complexity of the sequences with optimal autocorrelation magnitude constructed from the Legendre sequence pair or the twin-prime sequence pair is investigated. With the method proposed by Hu, we completely determine the 2-adic complexity of the sequences by calculating the exact autocorrelation distribution of the sequences and discussing the greatest common divisors. Results show that the 2-adic complexity of these sequences is either maximum or very close to maximum.

The symmetric 2-adic complexity of Tang-Gong interleaved sequences from Legendre sequence pair

“…then by Lemma 2.3, we have Different from the method used in [7], which determine the 2-adic complexity by using the autocorrelation distribution of the interleaved sequence itself, the autocorrelation and crosscorrelation distributions of the column sequences in the interleaved structure to determine the 2-adic complexity of v ′ is used instead in this paper.…”

“…In addition, Zhang et al [5] determined the 2-adic complexity of the Ding-Helleseth-Martinsen sequence by using "Gauss periods" and "Gauss sums". By using or generalizing above three methods, the 2-adic complexity of most binary sequences with good autocorrelation and some cycoltomic sequences have been determined [6][7][8][9].…”

“…Tang-Gong interleaved sequences constructed from the Legendre sequence pair have many good properties [7,11,12]. In this paper, we shall calculate the symmetric 2-adic complexity of these sequences.…”

“…In this paper, we shall calculate the symmetric 2-adic complexity of these sequences. Different from the use of the autocorrelation distribution of interleaved sequences in [7] to determine the 2-adic complexity of these sequences, we use the autocorrelation and crosscorrelation distributions of the column sequences of the interleaved structure to calculate their symmetric 2-adic complexity. Our result shows that these sequences have high symmetric 2-adic complexity to resist the attack of the RAA.…”

Improvements on the 4-adic complexity of a class of quaternary sequences

“…In order to avoid safety risks in communication and cryptography systems, it thus demands that the 4-adic complexity of a safe sequence s with period N should exceed N −16 6 , otherwise this sequence is so insecure that it can be decrypted by the RAA. In recent ten years, the research results of the 2-adic complexity of binary periodic sequences are rich [3,4,6,[15][16][17][18][19][20]25]. To the best of our knowledge, there are few literatures to study the 4-adic complexity of quaternary periodic sequences [2,13,14,21,22].…”