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Let p be a prime number , integer e ≥ 2 , Z / ??( pe ) is an integer mode pe residue class ring has a unique ring Z / ( pe ) on any sequence a p - adic rights bit resolution ( ? ) ai is {0 , 1 , ... , p ? 1 } on the sequence , they can be naturally regarded as the sequence in the Galois field GF (p) of the last century, the mid-1980s the Chinese scholars on the ring Z / ( pe ) primitive sequence compression export sequence , almost at the same time , scholars of the former Soviet Union also made the non-linear sequence model . after 20 years of research , in this type of non-linear sequence field of study , has achieved fruitful results of this study the Z / ( pe ) primitive sequence consists of the form xe - 1 the eta ( x0 , x1 , ... , xe - 2 ) compression function derived sequence of partial maintained its entropy , the following main results : 1 when p is an odd prime , if h ( x0 , x1 , ... , xe- 2 ) Xe ( ? ) ... x1 p - x0p ? coefficient ( p 1 ) / 2, then the Z / ( PE ) on primitive sequence shape such as XE - 1 eta ( x0 , x1 , ... , xe - 2 ) of the compression function of the derived sequence is a local security entropy , i.e. , given the Z / ( PE ) on a strong primitive polynomial f ( x ) , any two primitive sequences generated by f (x) on the set a, b ??is the Z / ( PE ) , if the presence of s ∈ Z / ( p ) , such that the sequence of ae - 1 eta ( a0 , a1 , ... , ae - 2 ) and be - 1 eta ( b0, b1 , ... , be- 2 ) in the position of the meet alpha ( t ) ≠ 0 t s value is the same, wherein alpha is Z / ( p ) by f ( x) and a0 is uniquely determined m- sequence, then a = b.2 when p = 2 , Z / ??( 2e ) primitive sequences from the form xe - 1 eta ( x0 , x1 , ... , xe -2 ) compression function derived sequence is the entropy local , i.e. Z / ( 2e ) on the strong primitive polynomial f ( x ) for a given set a , b is the Z / ( 2e ) by f (x) any two primitive sequence generated , if the presence of s ∈ Z / ( 2 ) , such that the sequence of AE - 1 eta ( a0 , a1 , ... , ae - 2 ) and be- 1 eta ( b0 , B1 , ... , be - 2) in the position of the meet alpha ( t ) ≠ 0 t s value is the same, where alpha is the Z / ( 2 ) , by f (x) and a0 is uniquely determined m- sequence , then a = b .
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