E. R. Berlekamp, "Goppa Codes", IEEE Trans. Inform. Theory 19, 1973, 590 -- 592. Home/Search Document Not in Database Summary Related Articles Check |
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On Minimal Realization Over a Finite Chain Ring. - Norton (2001) (Correct)
....this algorithm, see [5, 10] When there are zero divisors however, division based methods such as the Euclidean method fail. In this section we show how to solve the key equation over a nite chain ring. We rst simplify and generalize [13] to a commutative ring, using the key equation derived in [3]. 16 De nition 8.1 Let g; S 2 R[X ] 0 S g 1 and g monic. Then ( 2 R[X ] R[X ] 6= 0, solves the key equation if S (mod g) is monic and 1 g 1: If is minimal amongst all non zero solutions of the key equation, then ( is called a minimal solution. Throughout ....
Berlekamp, E.R. (1973). Goppa Codes. IEEE Trans. Information Theory 19, 590-592.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
.... Goppa [33] introduced a more general class of codes (containing the BCH codes as special case) for which decoding is based on the solution of the key equation F (x)u(x) q(x) mod G(x) for some polynomial G(x) Berlekamp s iterative algorithm does not work for arbitrary polynomial G(x) cf. [10]) Sugiyama et al. 73] suggested to solve this new key equation by application of the Euclidean algorithm for the determination of the greatest common divisor of F (x) and G(x) where the algorithm stops, when the polynomials u(x) and q(x) of appropriate degree are found. They also showed that ....
E. R. Berlekamp, \Goppa Codes", IEEE Trans. Inform. Theory 19, 1973, 590 - 592.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
....(5. 9) Goppa [33] introduced a more general class of codes (containing the BCH codes as special case) for which decoding is based on the solution of the key equation F (x)u(x) q(x) mod G(x) for some polynomial G(x) Berlekamp s iterative algorithm does not work for arbitrary polynomial G(x) cf. [10]) Sugiyama et al. 73] suggested to solve this new key equation by application of the Euclidean algorithm for the determination of the greatest common divisor of F (x)andG(x) where the algorithm stops, when the polynomials u(x) and q(x) of appropriate degree are found. They also showed that for ....
E. R. Berlekamp, "Goppa Codes", IEEE Trans. Inform. Theory 19, 1973, 590 -- 592.
Reaction Attacks Against Several Public-Key Cryptosystem - Hall, Goldberg, Schneier (1997) (12 citations) (Correct)
....one premise: If a (n, k) error correcting code is used which can correct t or fewer errors, then a decoder will not attempt to correct a vector which has t 1 or more errors. There are several decoders for Reed Solomon and Goppa codes which meet this criterion, including those described in [B73,P75,SKHN76]. A common component of each of these algorithms is that they work to find an error location polynomial #(z) of degree at most t. The decoders then determine the roots of #(z) in order to determine the location of the errors in the received vector (there is a one to one correspondance between the ....
E.R. Berlekamp, "Goppa Codes," IEEE Transactions on Information Theory, Vol. IT-19, No. 5, pp. 590--592, September 1973.
On the Security of Some Cryptosystems Based on Error-Correcting.. - Chabaud (1994) (9 citations) (Correct)
.... [SS92b] it is still not broken in its original description [McE78] Principle We assume that we have a (n; k) linear code on GF (2) described by its generator matrix G, for which we have a decoding algorithm that corrects at most t errors (the original description of McEliece uses Goppa codes [Ber73], On leave from D el egation G en erale de l Armement. Supported by the Centre National de Recherche Scientifique URA 1327. but the larger class of alternant codes [MS83] can also be used) We now choose at random some invertible matrix S and a permutation matrix P . The triplet (S; G; ....
E.R. Berlekamp. Goppa codes. IEEE Trans. Inform. Theory, IT-19(5):590-- 592, September 1973.
Some Aspects of Hankel Matrices in Coding Theory and Combinatorics - Tamm (2001) (2 citations) (Correct)
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E. R. Berlekamp, "Goppa Codes", IEEE Trans. Inform. Theory 19, 1973, 590 -- 592.
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