Abstract
In this paper, we discuss the relationship between the generation polynomial of a linear sequence and its decimation sequence over the finite field 𝔽2. Then we propose an upper bound of the number of terms in the generation polynomial of a decimation sequence of a linear sequence whose generation polynomial is trinomial. Finally, we suggest a method to calculate the terms of a decimation polynomial and their number directly, which can be used in the construction of irreducible polynomials with a controlled number of terms, when the source trinomial and the decimation distance satisfy a certain condition.
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