Research On Some Questions Of The K-error Linear Complexity For Pⁿ -Periodic Sequences

As an important standard to scale the stability of keystreams, once k-error linear complexity is proposed, widely attention is paid on it. This dissertation is mainly investigates some questions of the k-error linear complexity for pⁿ-periodic sequences, here p is a prime.If most sequences with period N have small k-error linear complexity for some small values of k, suquence with period N is not suitable for keystream with considering security. The entire stability of binary sequences with period 2ⁿ is investigated in chapter 2 accordingly, the minimal value k is given for which there are at least half of the sequences with period 2ⁿ have k-error linear complexity not larger than 2^n-1; Furthermore, such minimal value k is also studied for balanced sequences and imbalanced sequences with period 2ⁿ respectively.A strongly secure sequences should not only hold large linear complexity and k-error linear complexity, but also have less k-error sequences for some small values of k. The k-error sequences of pⁿ-periodic sequences over F_p is researched in chapter 3, the number of 1-error sequences of pⁿ-periodic sequences over F_p is given, and the number of 2-error sequences is discussed too; Further more, the expected value of the number of 1-error sequences of pⁿ-periodic sequences over F_p is also shown, here p is an odd prime.The k-error sequences of p^m-periodic sequences over F₂ is studied in chapter 4, the number of 1-error sequences of p^m-periodic sequences over F₂ is given; Further more, the expected value of the number of 1-error sequences of p^m-periodic sequences over F₂ is also shown, where p is an odd prime and 2 is a prime root of module p2.