Journal ArticleDOI
A division algorithm
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TLDR
In this paper, it was shown that a divisibility test for polynomials over a field in an intuitionistic setting may be thought of as a kind of division algorithm.Abstract:
A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitrary commutative ring R, we characterize those polynomials g such that the R-module endomorphism of R[X] given by multiplication by g has a left inverse.read more
Citations
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Patent
Low complexity sample adaptive offset encoding
TL;DR: In this paper, sample adaptive offset (SAO) is used to encode the largest coding unit (LCU) of a picture using a SAO mode, where the SAO is configured to calculate the differences between corresponding reconstructed samples of the LCU and original samples, clip a number of bits from each of the differences, sum the clipped differences to form a sum of differences.
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FPGA Implementation of an Improved OMP for Compressive Sensing Reconstruction
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System, method, and program for protecting cryptographic algorithms from side-channel attacks
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TL;DR: In this article, a system for protecting algorithms from side-channel attacks includes a digital processor having a first register, a second register, and a third register; an execution unit; and a processing unit.
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Using encapsulation headers to indicate internet protocol packet fragmentation in cellular networks
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TL;DR: In this article, a method of an aspect is performed in an Internet Protocol (IP) packet fragment reassembly system of a cellular network, which is one of reassembling IP packet fragments that are destined for wireless devices.
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Communication apparatus, method of checking received data size, multiple determining circuit, and multiple determination method
Fuyuta Sato,Hideo Okawa +1 more
TL;DR: In this paper, a packet length determining section determines that received data has a normal size, and notifies it to a discard determining section, until the subtraction result becomes a non-positive number and the quotient and the remainder match.
References
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Book
A Course in Constructive Algebra
TL;DR: In this paper, the authors present a generalization of the Dedekind-Hasse rings of algebraic fields to the setting of finite-rank free groups, and show that these groups can be represented by a set of polynomials.
Journal ArticleDOI
On the divisors of monic polynomials over a commutative ring.
Robert Gilmer,William Heinzer +1 more
Journal ArticleDOI
An algorithm for the divisors of monic polynomials over a commutative ring
TL;DR: Gilmer and Heinzer as mentioned in this paper proved that given a reduced ring R, a polynomial f can be divisible if and only if there exists a direct sum decomposition of R = R0 ⊕ Rm (m ≤ deg f), associated to a fundamental system of idempotents e0, …, em, such that the component of f in each Ri[X] has degree coefficient which is a unit of Ri.