L.: The first coordinate sequence of a linear recurring sequence of maximal period over Galois ring, Discrete Mat. L.: Analytical structure of linear recurring sequences, Fundamentalnaja i Prikladnaja Matematika (in Russian) 1(2) (1995), to appear. L.: Convolution of linear recurring sequences, Uspekhi Mat.
L.: Representations of linear recurring sequences and regular prime numbers, Uspekhi Mat. L.: Representations over rhe rings Z pn of a linear recurring sequences of maximal period over the field GF( p), Discrete Mat. L.: Representations over a field of a linear recurrence of maximal period over a residue ring, Uspekhi Mat. L.: Structure of Hopf algebras of linear recurring sequences, Uspekhi Mat. Kronecker, L.: Forlesungen über Zahlentheorie, 1, Teubner, Leipzig, 1901. Fundamental Algorithms, Addison-Wesley, New York, 1968.
E.: The Art of Computer Programming, Vol. Klove, Torleiv: Periodicity of recurring sequences in rings, Math. Jansson, B.: Random Number Generators, Almqvist and Wiksell, Stockholm, 1966. and Yoshida, W.: A simple derivation of Berlekamp-Massey algorithm and some applications, IEEE Trans. Ikai, T., Kosako, H., and Kojima, Y.: Subsequences in linear recurring sequences, Electronics Commun. Hall, M.: An isomorphism between linear recurring sequences and algebraic rings, Trans. Gill, A.: Linear Sequential Circuits, McGraw-Hill, New York, 1966. G.: Analysis of the Berlekamp-Massey linear feedback shift register synthesis algorithm, IBM J. Ring Theory, Springer-Verlag, New York, 1976. 33 (1931), 210–218.Įuler, L.: Introduction to calculus of infinitesimal variables (1748), Opera Omnia, Vol. T.: On sequences defined by linear recurrence relations, Trans. T.: Periodicity in sequences defined by linear recurrence relations, Proc. P.: General Solution of systems of linear homogeneous equations over commutative ring, Uspekhi Mat. P.: Systems of linear equations over commutative rings, Uspekhi Mat. 16 (1954), 331–342, 473–485.Įichenauer-Herrman, J., Grothe, H., and Lehn, J.: On the period length of pseudorandom vector-sequences generated by matrix generators, Math.
A.: Periodicity properties of recurring sequences, I, II, Indag. E.: Applied Modern Algebra, Macmillan, New York, 1978.ĭubois, D.: Modules of sequences of elements of a ring, J. 1, Carnegie Institute, Washington, D.C., 1919.ĭornhoff, L. E.: History of the Theory of Numbers, Vol. and Reiner, I.: Representation Theory of Finite Groups and Associative Algebras, Wiley, New York, London, 1962.ĭickson, L. J.: Periodicity over the ring of matrices, Fibonacci Quart. J.: A generalized Fibonacci seguence over an arbitrary ring, Fibonacci Quart. 473, Springer-Verlag, New York, 1991.ĭe, Carli, D. and Gollman, D.: Lower Bounds for the Linear Complexity of Sequences over Residue Rings, Lecture Notes in Comput. W., Taussky, O., and Ward, M.: Divisors of recurrent sequences, J. L.: Congruence Theory, Complete Words, Vol. L.: Theory of Probabilities, Lectures 1879–1880, Moscow, Leningrad, 1936, pp. and Piras, F.: On the continuous dual of a polynomial bialgebra, Comm. D.: On sequences of integers defined by recurrence relations, Quart. R.: Theory of Numbers, 3rd edn, Moscow, 1985.īrenner, J. 13(3) (1965), 902–912.īollman, D.: Some periodicity properties of modules over the ring of polynomials with coefficients in a residue class ring, SIAM J. C.: Modern Applied Algebra, McGraw-Hill, New York, 1970.īollman, D.: Some periodicity properties of transformations on vector space over residue class rings, J.
R.: Algebraic Coding Theory, McGraw-Hill, New York, 1968.īirkhoff, G. G.: Introduction to Commutative Algebra, Addison-Wesley, Mass., 1969.Īzumaya, G.: A duality theory for injective modules (Theory of quasi-Frobenius modules), Amer. S.: On distribution of frequencies of multigrams in linear recurring sequences over residue rings, Uspekhi Mat. Jungnickel, "Finite fields: Structure and arithmetics", Bibliographisches Inst. Blahut, "Theory and practice of error control codes", Addison-Wesley (1983)ĭ. Consequently, a periodic binary sequence with good randomness properties should have complexity close to the period length and a profile growing more or less smoothly. For a shift register sequence $\mathbf$ with period $N$ results in a linear complexity close to $N$, provided that $N$ is a power of $2$ or a Mersenne prime number (cf.
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