Reconstruction of a linear recurrence of maximal period over a Galois ring from its highest coordinate sequence
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A. S. Kuzmin
Abstract
Let R = GR (qn, qn) be a Galois ring of cardinality qn and characteristic pn, q = pr, p be a prime. We call a subset K ⊂ R a coordinate set if 0 ∈ K and for any a ∈ R there exists a unique ϰ(a) ∈ K such that a ≡ ϰ(a) (mod pR). Let u be a linear recurring sequence of maximal period (MP LRS) over a ring R. Then any its term u(i) admits a unique representation in the form
u(i) = w0(i) + pw1(i) + ⋯ + pn–1wn–1(i), wt(i) ∈ K, t ∈ {0, . . . , n – 1}.
We pose the following conjecture: the sequence u can be uniquely reconstructed from the sequence wn–1 for any choice of the coordinate set K. It is proved that such a reconstruction is possible under some conditions on K. In particular, it is possible for any K if R = Zpn and for any Galois ring R if K is a p-adic (Teichmüller) coordinate set.
© de Gruyter 2011
Articles in the same Issue
- Reconstruction of a linear recurrence of maximal period over a Galois ring from its highest coordinate sequence
- On properties of the Klimov–Shamir generator of pseudorandom numbers
- On the relationship between diagnostic and checking tests of the read-once functions
- Boolean functions without prediction
- Investigation of the behaviour of triangulations on simplicial structures
- On irredundant complexes of faces in the unit cube
Articles in the same Issue
- Reconstruction of a linear recurrence of maximal period over a Galois ring from its highest coordinate sequence
- On properties of the Klimov–Shamir generator of pseudorandom numbers
- On the relationship between diagnostic and checking tests of the read-once functions
- Boolean functions without prediction
- Investigation of the behaviour of triangulations on simplicial structures
- On irredundant complexes of faces in the unit cube
