2-Adic Complexity of Self-Shrinking Sequence

Abstract

This paper studies the 2-adic complexity of the self-shrinking sequence under the relationship between 2-adic integers and binary sequences. Based on the linear complexity and the number of the sequences which have the same connection integer, we conclude that the 2-adic complexity of the self-shrinking sequence constructed by a binary m-sequence of order n has a lower bound 2^n-2-1. Furthermore, it is shown that its 2-adic complexity has a bigger lower bound under some circumstances.