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**2005/241**

**Title:**

On the binary sequences with high GF(2) linear complexities and low GF(p) linear complexities

**Authors:**
Hao Chen, Liqing Xu

**Abstract:**

Klapper [1] showed that there are binary sequences of period q^n-1

(q is a prime power p^m, p is an odd prime)

with the maximal possible linear complexity q^n-1 when considered as sequences over GF(2), while the sequences

have very low linear complexities when considered as sequences over GF(p). This suggests that the binary sequences

with high GF(2) linear complexities and low GF(p) linear complexities are note secure in cryptography. In this note we

give some simple constructions of the binary sequences with high

GF(2) linear complexities and low GF(p) linear complexities. We

also prove some lower bounds on the GF(p) linear complexities of

binary sequences and a lower bound on the number of the binary

sequences with high GF(2) linear complexities and low GF(p)

linear

complexities .

**ePrint:**
https://eprint.iacr.org/2005/241

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