Residue polynomial systems
نویسندگان
چکیده
منابع مشابه
Polynomial Residue Systems via Unitary Transforms
A polynomial, A(z), can be represented by a polynomial residue system and, given enough independent residues, the polynomial can be reconstituted from its residues by the Chinese remainder theorem (CRT). A special case occurs when the discrete Fourier transform and its inverse realise the residue evaluations and CRT respectively, in which case the residue system is realised by the action of a m...
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Let be the quotient ring where is the finite field of size and is a positive integer. A Gray map of length over is a special map from to ( . The Gray map is said to be a ( )-Gray map if the image of any -constacyclic code over is a -constacyclic code over the field . In this paper we investigate the existence of ( )-Gray maps over . In this direction, we find an equivalent ...
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The polynomial residue number system (PRNS) has been considered as a useful tool for digital signal processing (DSP) since it can support parallel, carry-free, high speed arithmetic with minimum multiplication count provided that an appropriate modular ring is chosen. In this paper, the properties of two-dimensional (2-D) PRNS are investigated in detail. It is shown that in the 2-D PRNS system,...
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Let q > 1 be an integer and let a and b be elements of the residue ring ZZq of integers modulo q. We show how, when given a polynomial f ∈ ZZq[X] and approximations to v0, v1 ∈ ZZq such that v1 ≡ f(v0) mod q one can recover v0 and v1 efficiently. This result has direct applications to predicting the polynomial congruential generator: a sequence (vn) of pseudorandom numbers defined by the relati...
متن کاملCoupled systems of equations with entire and polynomial functions
We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1} A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We derive a priory estimates for the sums of the rootsof the considered system andfor the counting function of roots.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2002
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(00)00425-4