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

Abstract The symmetric 2-adic complexity of a class of Tang-Gong interleaved binary sequences with period 4N (where N ≡ 3 (mod 4)) constructed from the Legendre sequence pair is open (Yang et al., Designs, Codes and Cryptography, 2024, online first). By analysing the algebraic structure of the sequences and calculating the autocorrelation and crosscorrelation distributions of the column sequences in the interleaved structure, we completely determine the symmetric 2-adic complexity of the sequences. Our result shows that the symmetric 2-adic complexity of these sequences is equal to their 2-adic complexity.