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Linear Complexity, k-Error Linear Complexity, and the Discrete Fourier Transform
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Wilfried Meidl
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On the linear complexity for multidimensional sequences [PDF]
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and $k$-error linear complexity of multidimensional periodic sequences.
Gomez-Perez Domingo +2 more
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Linear complexity profiles and jump complexity
Information Processing Letters, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M Z Wang
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A relationship between linear complexity and k-error linear complexity
IEEE Transactions on Information Theory, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K.Kurosawa +3 more
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On the Teaching Complexity of Linear Sets
Theoretical Computer Science, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ziyuan Gao +2 more
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Linearization Method and Linear Complexity
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2008We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method.
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Periodic Sequences with Maximal Linear Complexity and Large k -Error Linear Complexity
Applicable Algebra in Engineering, Communications and Computing, 2003It is well known that sequences to be used as keystreams in stream ciphers should possess a large linear complexity. For cryptographic purposes, however, it is also required that altering a few terms of such a sequence should not cause a significant decrease in its linear complexity. This leads to the concept of \(k\)-error linear complexity.
Wilfried Meidl
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Linear Complexity of the Discrete Logarithm
Designs, Codes and Cryptography, 2003The authors prove several lower bounds on the linear complexity of finite sequences consisting of consecutive values of the discrete logarithm modulo a prime. The method and the results are new and deserve highest notice in mathematical cryptography. In particular, several previously known results are improved.
Konyagin, S. +2 more
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IEEE Transactions on Information Theory, 2002
Summary: Rueppel (1986) conjectured that periodic binary sequences have expected linear complexity close to the period length \(N\). In this paper, we determine the expected value of the linear complexity of \(N\)-periodic sequences explicitly and confirm Rueppel's conjecture for arbitrary finite fields.
Meidl, W., Niederreiter, H.
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Summary: Rueppel (1986) conjectured that periodic binary sequences have expected linear complexity close to the period length \(N\). In this paper, we determine the expected value of the linear complexity of \(N\)-periodic sequences explicitly and confirm Rueppel's conjecture for arbitrary finite fields.
Meidl, W., Niederreiter, H.
exaly +3 more sources
Complexity of Linear Boolean Operators
Foundations and Trends® in Theoretical Computer Science, 2013How to compute a linear Boolean operator by a small circuit using only unbounded fanin addition gates? Because this question is about one of the simplest and most basic circuit models, it has been considered by many authors since the early 1950s. This has led to a variety of upper and lower bound arguments—ranging from algebraic (determinant and matrix
Stasys Jukna, Igor Sergeev
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