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Bibliography

[AS] W. Adams and D. Shanks, ``Strong primality tests that are not sufficient,'' Math. Comp. 39 (1982), no. 159, 255-300.

[Ar] M. Artin, Algebra, Prentice-Hall, 1991

[Art] J. Arthur, ``Automorphic representations and number theory'', 1980 Seminar on Harmonic Analysis, (C. Herz, R. Rigelhof, ed.), CMS Conf. Proc. vol 1, 1981.

[Ash] R. Ash, Information theory, Dover, 1965

[AK] E. Assmus, J. Key, Designs and their codes, Cambridge University Press, 1992

[AM] E. Assmus, Jr. and H. Mattson, ``On the automorphism groups of Paley-Hadamard matrices", in Combinatorial mathematics and its applications, ed. R. Bose, T. Dowling, Univ of North Carolina Press, Chapel Hill, 1969

[B] E. Berlekamp, ``Block coding with noiseless feedback,'' PhD Thesis, Dept EE, MIT, 1964

[BCG] Berlekamp, J. Conway, R. Guy, Winning ways, II, Academic Press, 1982

[BC] W. W. R. Ball and H. S. M. Coxeter, Mathematical recreation and essays, 13th ed, Dover, 1987

[BFR] E. Bonsdorff, K. Fabel, O. Riihimaa, Schach und zahl, Walter Rau Verlag, Düsseldorf, 1966

[BS] E. Bach and J. Shallit, Algorithmic number theory, vol I, MIT Press, 1997

[BG] I. Blake and I. Gibson, ``Decoding the binary Golay code with miracle octad generators,'' IEEE Trans. Infor. Theory 24(1978)261-264.

[Br] J. Bruce, ``A really trivial proof of the Lucas-Lehmer test,'' Amer. Math. Monthly, April 1993, pages 370-371.

[Bu] B. Buchburger, ``Gröbner bases: an algorithmic method in polynomial ideal theory'', in N. Bose (ed.), Multidimensional systems theory, D. Reidel Pub. Co., 1985

[C] John H. Conway, On numbers and games, Academic Press, 1976

[CS] J. Conway and N. Sloane, Sphere packings, lattices, and groups, Springer-Verlag, 1993

[CS2] ---, ``Lexicographic codes: error-correcting codes from game theory'', IEEE Transactions on Information Theory, 32(1986)337-348

[CSW] --- and A. Wilks, ``Gray codes and reflection groups'', Graphs and combinatorics 5(1989)315-325

[CLO] D. Cox, J. Little, D. O'Shea, Ideals, varieties, and algorithms, Springer-Verlag book link

[CCNPW] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, ``M12,'' in Atlas of Finite Groups, Clarendon Press, Oxford, 1985. web page

[CFS] G. Cooperman, L. Finkelstein and N. Sarawagi, ``Applications of Cayley graphs", in Applied algebra..., Springer-Verlag, Lecture Notes in Computer Science, 508, 1990

[CG] S. Curran and J. Gallian, ``Hamiltonian cycles and paths in Cayley graphs and diagraphs - survey", Discrete Math. 156(1996)1-18

[CL] archives of the cube-lovers list at http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/

[Co] J. Cosgrave, ``Number Theory and Cryptography (using Maple),'' in Coding Theory and Cryptology: From Enigma and Geheimschreiber to Quantum Theory (ed. D. Joyner), New York: Springer Verlag, Lecture Notes in Computational Science and Engineering (1999) book link

[Cu] R. Curtis, ``The Steiner system S(5,6,12), the Mathieu group M12, and the kitten,'' in Computational group theory, ed. M. Atkinson, Academic Press, 1984.

[E] J. Ellis, ``The history of non-secret encryption,'' Cryptologia, Volume XXIII Number 3 (July 1999) , 267-273

[FKL] M. Fossorier, Y. Kou, S. Lin, ``Low density parity check codes based on finite geometries: a rediscovery and new results,'' IEEE Trans. Info. Theory 47(2001)27111-2736

[FS] A. Frey and D. Singmaster, Handbook of cubik math, Enslow Pub., 1982

[FST] T. Fuja, D. Srihara, R. M. Tanner, ``A class of group-structured LDPC codes,'' preprint paper link

[Ga] R.G. Gallagher, ``Low density parity check codes,'' IRE Trans. Info. Theory 8(1962)21-28

[GAP] The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.2; 2000, http://www.gap-system.org.

[Gar1] M. Gardner, ``Combinatorial card problems'' in Time travel and other mathematical bewilderments, W. H. Freeman, New York, 1988

[Gol] S. Golomb, Shift register sequences, Aegean Park Press, Laguna Hills, Ca, 1967

[Go] V. D. Goppa, Geometry and codes, Kluwer, 1988.

[G] A. Granville, ``Zaphod Beeblebrox's brain and the fifty-ninth row of Pascal's triangle,'' Amer. Math. Monthly, April 1992, pp 318-331

[GJ] M. Garey and D. Johnson, Computers and intractibility, W. H. Freeman, New York, 1979

[GK1] A. Klapper and M. Goresky, ``2-adic shift registers,'' in Fast Software Encryption (Springer Lecture Notes in Computer Science, 1995), New York, NY, pp. 170-178

[GK2] A. Klapper and M. Goresky, ``Feedback shift registers, 2-adic span, and combiners with memory,'' Journal of Cryptology 10 (1997) 111-147. papers link

[HHLO] Heikki Hamalainen, Iiro Honkala, Simon Litsyn, Patric Ostergard, ``Football Pools-A Game for Mathematicians,'' American Mathematical Monthly, Vol. 102, No. 7. (Aug. - Sep., 1995), pp. 579-588.

[HW] G. Hardy and E. Wright, An introduction to the theory of numbers, $ 5^{th}$ ed, Oxford Univ Press, 1979 book link

[Her] I. N. Herstein, Abstract algebra, 3-rd ed., Prentice Hall, 1996.

[Hi] R. Hill, ``Searching with lies,'', in Surveys in Combinatorics, ed. by P. Rowlinson, London Math Soc, Lecture Notes Series # 218

[H] D. Hofstadler, Metamathematical themas, Basics Books, 1985 (Mostly a collection of Scientific American columns he wrote; the articles referred to here were also published in Scientific American, March 1981, July 1982)

[Hum] J. Humphreys, Reflection groups and coxeter groups, Cambridge Univ Press, 1990

[J1] D. Joyner, Adventures in group theory, Johns Hopkins Unv. Press, 2002. book link

[J2] ---, golay12.g package, at golay GAP code

[Kn] D. Knuth, The art of computer programming: volume 2, 3rd edition, Addison-Wesley-Longman, 1998 book link

[K] R. Kreminski

[LR] J. Lafferty, D. Rockmore, ``Spectral techniques for expander codes,'' preprint paper link

[La] S. Lang, Algebra, 2-nd ed., Addison-Wesley, 1984.

[LP] R. Lidl, G. Pilz, Applied abstract algebra, 2-nd ed., Springer, 1998.

[Lu] A. Luers, ``The group structure of the pyraminx and the dodecahedral faces of M12", USNA Honors thesis, 1997 (Advisor W. D. Joyner) paper link

[Mac] D. MacKay, ``Good error-correcting codes based on very sparse matrices,'' IEEE Trans. Info. Theory 45 (1999)399-431 (errata: 47(2001)2101)

[MN] ---, R. Neal, ``Near Shannon limit performance of low density parity check codes,'' preprint, 1996 (appeared in Electronic Letters)

[MS] F. MacWilliams and N. Sloane, The theory of error-correcting codes, North-Holland, 1977. See also N. Sloane's web site

[MAGMA] W. Bosma, J. Cannon, C. Playoust, ``The MAGMA algebra system, I: The user language,'' J. Symb. Comp., 24(1997)235-265.
See also the MAGMA homepage

[Magma1] W. Bosma, J. Cannon, C. Playoust, A. Steel, Solving problems with MAGMA, Univ Sydney, 1999.

[Magma2] J. Cannon, C. Playoust, An introduction to algebraic programming with MAGMA, Univ Sydney, 1999.

[MKS] W. Magnus, A. Karrus and D. Solitar, Combinatorial group theory, 2nd ed, Dover, 1976

[MOV] Alfred J. Menezes, Paul C. Van Oorschot, Scott A. Vanstone Handbook of applied cryptography, CRC Press Series on Discrete Mathematics and Its Applications, CRC Press, 1996. book link

[Mont] J. Montague, ``Searching with lies'', USNA Honors thesis, 1998 Available on the web at paper link

[MZ] G. Marsaglia and A. Zaman, ``A new class of random number generators,'' Annals of Applied Probability 1(1991)462-490

[NG] G. Nakos and N. Glinos, ``Computing Gröbner bases over Z'', Mathematica Journal, ...

[NJ] G. Nakos and D. Joyner, Linear algebra and applications, Brooks-Cole, 1998

[N] I. Niven, ``Coding theory applied to a problem of Ulam,'' Math Mag 61(1988)275-281

[NST] P. Neumann, G. Stoy and E. Thompson, Groups and geometry, Oxford Univ. Press, 1994

[Pim] A. Pimlott, ``How to get rich off Finnish football fans,'' Harvard Tangents, issue 1.1, 1994

[Pl] V. Pless, ``Decoding the Golay codes,'' IEEE Trans. Infor. Theory 32(1986)561-567.

[P] O. Pretzel, Codes and algebraic curves, Oxford Lecture Series, vol 9, Clarendon Press, Oxford, 1998

[RSA] R.L. Rivest, A. Shamir, and L.M. Adleman, ``A method for obtaining digital signatures and public-key cryptosystems,'' Communications of the ACM, 21(February 1978), 120-126

[Ro] G. Robin, ``Grandes valuers de la fonction somme des diviseurs et hypthése de Riemann,'' J. Math. Pures Appl. 63(1984)187-213.

[Rom] Steven Roman, Coding and information theory, Springer-Verlag, 1992

[R] J. J. Rotman, An introduction to the theory of groups, 4th ed, Springer-Verlag, Grad Texts in Math 148, 1995

[Sch] M. R. Schroeder, Number theory in science and communication, 3-rd ed., Springer, 1997.

[Ser] J.-P. Serre, Trees, Springer-Verlag, 1980

[Si] D. Singmaster, Notes on Rubik's magic cube, Enslow, 1981

[SING] SINGULAR, A Computer Algebra System for Polynomial Computations. See the SINGULAR homepage

[Sp] D. Spielman, ``Linear time encodable and decodable error-correcting codes,'' IEEE Trans. Info. Theory 42(1996)1723-1731

[St] H. Stark, ``A complete determination of the complex quadratic fields of class-number one,'' Michigan Math. J. 14(1967)1-27.

[TW] A. D. Thomas and G. V. Wood, Group tables, Shiva Publishing Ltd, Kent, UK, 1980

[Th] W. Thurston, ``Conway's tiling groups,'' Amer. Math. Monthly 97 (1990)757-773

[U] S. Ulam, Adventures of a mathematician, Scribner and Sons, New York, 1976

[vdP] A. J. van der Poorten, ``Notes on continued fractions and recurrence sequences,'' in Number theory and cryptography (ed. J. H. Loxton), London Math Soc. Lecture Notes, Cambridge Univ Press, 1990

[Va] R. C. Vaughan, The Hardy-Littlewood method, Cambridge Univ. Press, 1981

[Wa] W. P. Wardlaw, ``The RSA Public Key Cryptosystem,'' in Coding Theory and Cryptology: From Enigma and Geheimschreiber to Quantum Theory (ed. D. Joyner), New York: Springer Verlag, Lecture Notes in Computational Science and Engineering (1999) book link

[Wh] White, Arthur, ``Fabian Stedman: The First Group Theorist?", American Mathematical Monthly, Nov. 1996, pp771-8.


David Joyner 2002-08-23

Last updated 5-14-2004.