The minimum, maximum and average number of arithmetic operations both on polynomials and in the ground field are derived. We consider five different algorithms to compute gcd(A 1, A 2) where A 1, A 2∈ Z 2[ x] have degrees m≥n≥0. Compared with the classical Euclidean algorithm that...
PolynomialsReed-Solomon codesThis paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps taken to perform the Generalized Minimum Distance decoding are similar to those performed by the ...
2.Research of RS decoding based onmodified Euclidean algorithm基于改进型欧几里德算法的RS译码研究 3.According to the complexity of decoding circuit in digital TV and the moderate speed of decoding,amodified Euclidean algorithmis proposed based on the related deduction of division with reminder of pol...
An algorithm of Euclidean polynomial factorization and the theory of two-channel filter banks with low delay are discussed in this paper. Euclid多项式分解算法可以用于滤波器组的设计,该文首先讨论了Euclid分解算法与低时延两通道完全重构的滤波器组设计理论,推导出可实现分解的条件,并从理论上加以证明,由于Eu...
Subsets of a Euclidean domain are characterised with the following objectives: (1) en- suring uniqueness of the quotient and remainder in the Division Algorithm; (2) permit- ting unique base expansion with respect to any nonzero nonunit in the ring; (3) allowing explicit solutions to B´ez...
the error-locator polynomials are expressed for v = 1, 2 as specific examples that are important in applications. Furthermore, a decoding algorithm is proposed that corrects t + v errros, which exceeds the BCH bound, by estimating the undetermined polynomials. the proposed algorithm requires O(...
Let R[X] be theEuclidean ringof polynomials over the field of real numbers with the Euclidean function [phi](f) = deg(f) for each nonzero element f [member of] R[X]. Recall that for any nonzero element r in aEuclidean ringR with Euclidean function [phi], [phi]([1.sub.R]) [...
1. Use the Euclidean algorithm to find greatest common divisor of f (x) = x^4 + 7 x^2 + 1 and g (x) = x^5 + 2, considered as polynomials in F_3 [x]. Express gcd(f, g) as a combination of f and g. 2. P What is the reciprocal of 15 expressed as a fraction?
摘要: This paper presents a method to determine a set of basis polynomials from the extended Euclidean algorithm that allows Generalized Minimum Distance decoding of Reed-Solomon codes with a complexity of O(nd).关键词: Reed-Solomon codes communication complexity decoding polynomials Reed-Solomon ...
In this short note, we extend Faug茅re's F4-algorithm for computing Gr?bner bases to polynomial rings with coefficients in an Euclidean ring. Instead of successively reducing single S-polynomials as in Buchberger's algorithm, the F4-algorithm is based on the simultaneous reduction of several ...