1. What are the contributions in this paper?
In this paper the authors extend the algorithm to the case when the elements of the sequence are integers modulo m, where m is an arbitrary integer with known prime decomposition.
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Shift-Register Synthesis (Modulo m)
James A. Reeds,Neil J. A. Sloane +1 more
TL;DR: In this paper, a generalization of Berlekamp's algorithm to the case when the elements of the sequence are integers modulo m, where m is an arbitrary (but known) integer, is presented.
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Abstract: The Berlekamp algorithm takes a sequence of elements from a field and finds the shortest linear recurrence (or linear feedback shift register) that can generate the sequence. We present an algorithm which generalizes Berlekamp’s to the case when the elements of the sequence are integers modulo m, where m is an arbitrary (but known) integer. Details will be published elsewhere.
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Citations
Discrete logarithms in finite fields and their cryptographic significance
Andrew Odlyzko
- 01 Dec 1985
TL;DR: This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2n), finding that in order to be safe from attacks using these algorithms, the value of n for which GF( 2n) is used in a cryptosystem has to be very large and carefully chosen.
New array codes for multiple phased burst correction
Mario Blaum,Ron M. Roth +1 more
TL;DR: An optimal family of array codes over GF(q) for correcting multiple phased burst errors and erasures, where each phased burst corresponds to an erroneous or erased column in a code array, is introduced.
211
True Random Number Generators
Mario Stipčević,Çetin Kaya Koç +1 more
- 01 Jan 2014
TL;DR: This chapter discusses several examples where use of a true RNG is critical and shows how it can significantly improve security of cryptographic systems, and discusses industrial and research challenges that prevent widespread use of TRNGs.
188
On the Hamming distance of linear codes over a finite chain ring
Graham H. Norton,Ana Sălăgean +1 more
TL;DR: The Hamming weight enumerator of a free MDS code over R is computed and it is shown that in general d(C)/spl les/d(C~) with equality for free codes (i.e., for free R-submodules of R/sup n/) and in particular for Hensel lifts of cyclic codes over K.
On recursiveness and related topics in linear systems
TL;DR: A decomposition of matrix formal power series (linear systems) is developed and the interconnections between formal powerseries, realization, recursiveness, andBerlekamp-Massey algorithm are revealed.
112
References
•Book
Algebraic Coding Theory
Elwyn R. Berlekamp
- 01 Jan 2015
TL;DR: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
3.1K
Shift-register synthesis and BCH decoding
TL;DR: It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback shift register capable of generating a prescribed finite sequence of digits.
2.4K
•Book
Continued Fractions: Analytic Theory and Applications
William B. Jones,W. J. Thron +1 more
- 09 Mar 2009
TL;DR: In this paper, the authors present a method for representing analytic functions by continued fractions and apply it to the birth-death process (BDP) in the context of continuous fractions.
786
•Book
The theory of information and coding
Robert J. McEliece
- 01 Jan 1977
TL;DR: In this paper, the authors present a survey of advanced topics for part I and a survey for part II of a survey on the Gaussian channel and the source coding theorem, including linear codes, BCH Goppa codes, and variable-length source coding.
761
A method for solving key equation for decoding goppa codes
TL;DR: It is shown that the key equation for decoding Goppa codes can be solved using Euclid's algorithm, and the error locator polynomial is proved the multiplierPolynomial for the syndrome poynomial multiplied by an appropriate scalar factor.
451