Linear Recurring Sequences

Previous article Next article Linear Recurring SequencesNeal ZierlerNeal Zierlerhttps: //doi. org/10. 1137/0107003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 A. A. Albert, Fundamental Concepts of Higher Algebra, Univ. of Chicago Press, 1956 0073. 00802 Google Scholar2 J. L. Brenner, Linear recurrence relations, Amer. Math. Monthly, 61 (1954), 171–173 MR0059934 0055. 03508 CrossrefGoogle Scholar3 W. H. Bussey, Galois field tables for p^n169, Bull. Amer. Math. Soc. , 12 (1905), 22–38 CrossrefGoogle Scholar4 W. H. Bussey, Galois field tables of order less than 1000, Bull. Amer. Math. Soc. , 16 (1909), 188–206 CrossrefGoogle Scholar5 R. D. Carmichael, A Simple Principle of Unification in the Elementary Theory of Numbers, Amer. Math. Monthly, 36 (1929), 132–143 MR1521682 CrossrefGoogle Scholar6 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 Scholar7 Randolph Church, Tables of irreducible polynomials for the first four prime moduli, Ann. of Math. (2), 36 (1935), 198–209 MR1503219 0011. 00501 CrossrefGoogle Scholar8 G. E. Forsythe, , H. H. Germond and, A. S. Householder, Monte Carlo Methods, Nat. Bur. Standards. Appl. Math. Ser. , 12, 1951 Google Scholar9 Marshall Hall, An isomorphism between linear recurring sequences and algebraic rings, Trans. Amer. Math. Soc. , 44 (1938), 196–218 MR1501967 0019. 19301 CrossrefGoogle Scholar10 C. Jordan, The Calculus of finite differences, Chelsea, New York, 1950 0041. 05401 Google Scholar11 R. Lerner, Signals having uniform ambiguity functions, I. R. E. Convention Record, Information Theory Section, New York, 1958, March Google Scholar12 Oystein Ore, Contributions to the theory of finite fields, Trans. Amer. Math. Soc. , 36 (1934), 243–274 MR1501740 0009. 10003 CrossrefGoogle Scholar13 R. Price and, P. E. Green, Jr. , An anti-multipath communication system, Proc. I. R. E. , to appear Google Scholar14 Raphael M. Robinson, Mersenne and Fermat numbers, Proc. Amer. Math. Soc. , 5 (1954), 842–846 MR0064787 0058. 27504 CrossrefISIGoogle Scholar15 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 Scholar16 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 Scholar17 Morgan Ward, The arithmetical theory of linear recurring series, Trans. Amer. Math. Soc. , 35 (1933), 600–628 MR1501705 0007. 24901 CrossrefGoogle Scholar18 Edwin Weiss and, Neal Zierler, Locally compact division rings, Pacific J. Math. , 8 (1958), 369–371 MR0121432 0087. 03101 CrossrefGoogle Scholar19 Neal Zierler, A decomposition theorem for the integers modulo q, Amer. Math. Monthly, 65 (1958), 31–32 MR0098084 0103. 27204 CrossrefGoogle Scholar20 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. Shehadeh28 July 2006 | SIAM Journal on Applied Mathematics, Vol. 16, No. 5AbstractPDF (444 KB) Linear Recursive Sequences18 July 2006 | SIAM Review, Vol. 10, No. 3AbstractPDF (1184 KB) A New Class of Cyclic CodesDouglas R. Anderson12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 16, No. 1AbstractPDF (1580 KB) Characteristic Linear Sequences and Their Coset FunctionsRobert Gold13 July 2006 | SIAM Journal on Applied Mathematics, Vol. 14, No. 5AbstractPDF (606 KB) Linear Codes of Constant WeightE. Weiss13 July 2006 | SIAM Journal on Applied Mathematics, Vol. 14, No. 1AbstractPDF (561 KB) Simultaneous Error-Correction and Burst-Error Detection Using Binary Linear Cyclic CodesEdward C. Posner13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 4AbstractPDF (962 KB) Some Periodicity Properties of Transformations on Vector Spaces Over Residue Class RingsDorothy A. Bollman13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 3AbstractPDF (716 KB) Random Number Generators1 August 2006 | SIAM Review, Vol. 4, No. 3AbstractPDF (3435 KB) A Class of Error-Correcting Codes in pᵐ SymbolsDaniel Gorenstein and Neal Zierler10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 2AbstractPDF (691 KB) Polynomial Codes Over Certain Finite FieldsI. S. Reed and G. 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