The cube theory for 2nperiodic binary sequences
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The linear complexity and kerror linear complexity of a sequencehave been used as important measures for keystream strength, hencedesigning a sequence with high linear complexity and kerrorlinear complexity is a popular research topic in cryptography. In order to study kerror linear complexity of binarysequences with period 2n, a new tool called cube theory isdeveloped. In this paper, we first give ageneral decomposition approach to decompose a binary sequence with period 2n into some disjoint cubes. Second, a countingformula for mcubes with the same linear complexity is derived, which is equivalent to the counting formula for kerror vectors. The counting formulaof 2nperiodic binary sequences which can be decomposedinto more than one cube is also investigated, which extends an important result by Etzion et al.
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