Abstract
Sequences with high linear complexity property are of importance in applications. In this paper, based on the theory of generalized cyclotomy, new classes of quaternary generalized cyclotomic sequences with order 4 and period 2pm are constructed. In addition, we determine their linear complexities over finite field F4 and over ℤ4, respectively.
Highlights
Pseudorandom sequence has a wide range of applications in the spread spectrum communication, radar navigation, code division multiple access, stream cipher, and so on [1]. e linear complexity L({s(u)}) of a sequence {s(u)} is defined as the smallest order of linear feedback shift register (LFSR) that can generate the whole sequence
Sequences with high linear complexity can be constructed based on cyclotomic classes
Sequences based on classical cyclotomic classes and generalized cyclotomic classes are called classical cyclotomic sequences and generalized cyclotomic sequences, respectively. ere are lots of works on linear complexity of binary cyclotomic sequences, see [4,5,6,7], for instance
Summary
Pseudorandom sequence has a wide range of applications in the spread spectrum communication, radar navigation, code division multiple access, stream cipher, and so on [1]. e linear complexity L({s(u)}) of a sequence {s(u)} is defined as the smallest order of linear feedback shift register (LFSR) that can generate the whole sequence. In [19], Edemskiy and Ivanov constructed another kind of new quaternary generalized cyclotomic sequences with period 2p based on the Chinese Remainder eorem and studied their autocorrelation properties and linear complexities over F4 as well as Z4. The sequence they constructed are both quaternary sequences, it can be seen by comparison that [16, 17, 19] have their advantages and disadvantages. The difference between these two constructions is that, in [19], the sequences were constructed by using the Chinese Remainder eorem, while the sequences in this paper are defined directly. erefore, this paper can be regarded as a generalization of [19]
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