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Linear Recurring Sequences

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1959

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Previous article Next article Linear Recurring SequencesNeal ZierlerNeal Zierlerhttps://doi.org/10.1137/0107003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. A. Albert, Fundamental Concepts of Higher Algebra, Univ. of Chicago Press, 1956 0073.00802 Google Scholar[2] J. L. Brenner, Linear recurrence relations, Amer. Math. Monthly, 61 (1954), 171–173 MR0059934 0055.03508 CrossrefGoogle Scholar[3] W. H. Bussey, Galois field tables for $p^{n}\leqq{169}$, Bull. Amer. Math. Soc., 12 (1905), 22–38 CrossrefGoogle Scholar[4] W. H. Bussey, Galois field tables of order less than 1000, Bull. Amer. Math. Soc., 16 (1909), 188–206 CrossrefGoogle Scholar[5] R. D. Carmichael, A Simple Principle of Unification in the Elementary Theory of Numbers, Amer. Math. Monthly, 36 (1929), 132–143 MR1521682 CrossrefGoogle Scholar[6] Claude Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, Mathematical Surveys, No. VI, American Mathematical Society, New York, N. Y., 1951xi+188 MR0042164 0045.32301 CrossrefGoogle Scholar[7] Randolph Church, Tables of irreducible polynomials for the first four prime moduli, Ann. of Math. (2), 36 (1935), 198–209 MR1503219 0011.00501 CrossrefGoogle Scholar[8] G. E. Forsythe, , H. H. Germond and , A. S. Householder, Monte Carlo Methods, Nat. Bur. Standards. Appl. Math. Ser., 12, 1951 Google Scholar[9] Marshall Hall, An isomorphism between linear recurring sequences and algebraic rings, Trans. Amer. Math. Soc., 44 (1938), 196–218 MR1501967 0019.19301 CrossrefGoogle Scholar[10] C. Jordan, The Calculus of finite differences, Chelsea, New York, 1950 0041.05401 Google Scholar[11] R. Lerner, Signals having uniform ambiguity functions, I.R.E. Convention Record, Information Theory Section, New York, 1958, March Google Scholar[12] Oystein Ore, Contributions to the theory of finite fields, Trans. Amer. Math. Soc., 36 (1934), 243–274 MR1501740 0009.10003 CrossrefGoogle Scholar[13] R. Price and , P. E. Green, Jr., An anti-multipath communication system, Proc. I.R.E., to appear Google Scholar[14] Raphael M. Robinson, Mersenne and Fermat numbers, Proc. Amer. Math. Soc., 5 (1954), 842–846 MR0064787 0058.27504 CrossrefISIGoogle Scholar[15] W. McC. Siebert, A radar detection philosophy, Trans. I.R.E. (Information Theory), IT-2 (1956), 204–221, Sept. 10.1109/TIT.1956.1056805 CrossrefISIGoogle Scholar[16] B. L. van der Waerden, Modern Algebra. Vol. I, Frederick Ungar Publishing Co., New York, N. Y., 1949xii+264, and 1953 MR0029363 0039.00902 Google Scholar[17] Morgan Ward, The arithmetical theory of linear recurring series, Trans. Amer. Math. Soc., 35 (1933), 600–628 MR1501705 0007.24901 CrossrefGoogle Scholar[18] Edwin Weiss and , Neal Zierler, Locally compact division rings, Pacific J. Math., 8 (1958), 369–371 MR0121432 0087.03101 CrossrefGoogle Scholar[19] Neal Zierler, A decomposition theorem for the integers modulo q, Amer. Math. Monthly, 65 (1958), 31–32 MR0098084 0103.27204 CrossrefGoogle Scholar[20] Neal Zierler, On the theorem of Gleason and Marsh, Proc. Amer. Math. Soc., 9 (1958), 236–237 MR0094332 0090.24202 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The Fast m-Transform: A Fast Computation of Cross-Correlations with Binary m-Sequences13 July 2006 | SIAM Journal on Computing, Vol. 20, No. 4AbstractPDF (798 KB)Doubly-Periodic Sequences and Two-Dimensional RecurrencesSteven Homer and Jerry Goldman2 August 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 6, No. 3AbstractPDF (1147 KB)Factoring Polynomials over a Finite FieldMichael Willett12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 35, No. 2AbstractPDF (527 KB)The Index of an M-SequenceMichael Willett28 July 2006 | SIAM Journal on Applied Mathematics, Vol. 25, No. 1AbstractPDF (328 KB)On the Distribution of the Coefficients of Some PolynomialsNazmi M. 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Solomon10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 2AbstractPDF (430 KB) Volume 7, Issue 1| 1959Journal of the Society for Industrial and Applied Mathematics History Submitted:19 December 1957Published online:10 July 2006 InformationCopyright © 1959 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0107003Article page range:pp. 31-48ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

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