Compressing Mappings on Primitive Sequences over Z/(2) and Its Galois Extension |
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Authors: | Qi Wenfeng Zhu Xuanyong |
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Institution: | Department of Applied Mathematics, Zhengzhou Information Engineering University, 1001-745, Zhengzhou, 450002, People's Republic of Chinaf1f2 |
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Abstract: | Let f(x) be a strongly primitive polynomial of degree n over Z/(2e), η(x0,x1,…,xe−2) a Boolean function of e−1 variables and (x0,x1,…,xe−1)=xe−1+η(x0,x1,…,xe−2)G (f(x),Z/(2e)) denotes the set of all sequences over Z/(2e) generated by f(x), F2∞ the set of all sequences over the binary field F2, then the compressing mapping
Full-size image is injective, that is, for
,
G(f(x),Z/(2e)),
=
if and only if Φ(
)=Φ(
), i.e., (
0,…,
e−1)= (
0,…,
e−1) mod 2. In the second part of the paper, we generalize the above result over the Galois rings. |
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Keywords: | primitive polynomial Galois ring linear sequence compressing mapping |
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