On the symmetric 2-adic complexity of periodic binary sequences

Abstract

Symmetric 2-adic complexity is a better measure for assessing the strength of a periodic binary sequence against the rational approximation attack. We study the symmetric 2-adic complexity of the sequences with known 2-adic complexity. To this end, we propose an equivalent definition of the symmetric 2-adic complexity and two sufficient conditions for a periodic sequence to achieve the maximum symmetric 2-adic complexity. As a first application, several types of sequences with maximum 2-adic complexity are easily shown to have the maximum symmetric 2-adic complexity. In addition, with the new definition, by analysing the algebraic structure of the sequences and applying the method for the calculation of their 2-adic complexity, we determine the symmetric 2-adic complexity of the Ding-Helleseth-Martinsen sequence and the sequence constructed by interleaving a pair of Legendre sequences.