Group rings for communications

[1] N. N. Azenb er, A. A. Bovdi, E. I. Gergo and F. E. Geche, Algebraic asp ects of threshold logic, (Russian), Cybernetics, no. 2 (1980) 26-30.

[2] O. M. Baksalary, D. S. Bernstein and G. Trenkler, On the equality b etween rank and trace of an idemp otent matrix, Appl. Math. Comput., 217 (2010) 4076-4080.

[3] S. Bellovin and F. Miller, Inventor of One-Time pad, Cryptologia, 35 no. 3 (2011) 203-222.

[4] R. E. Blahut, Algebraic Codes for data transmission, Cambridge University Press, 2003.

[5] N. Boston, Applications of Algebra to Communications, Control and Signal Pro cessing, Springer, 2012.

[6] S. Buckley, Why do research in pure mathematics?, Irish Math. Soc. Bul letin, no. 72 2013 39-44.

[7] E. Candes, J. Romb erg and T. Tao, Robust Uncertainty Principles: Exact Signal Reconstruction From Highly
Incomplete Frequency Information, IEEE Trans. Inform. Theory , 52 no. 2 (2006) 489-509.

[8] C. Carlet and Y. Tan, On Group Rings and some of their applications to combinatorics and symmetric Cryptography, these pro ceedings.

[9] C. Curtis and I. Reiner, Representation Theory of Finite Groups and Asso ciative Algebras,Amer. Math. Soc., 1962.

[10] P. Davis, Circulant matrices, AMS Chelsea Publishing, 1994.

[11] W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. Information Theory, 22 no. 6 (1976) 644-654.

[12] B. Ho chwald and W. Sweldens, Differential unitary space time mo dulation, IEEE Trans. Comm., 48 (2000) 2041-2052.

[13] R. J. Evans and I. M. Isaacs, Generalized Vandermonde determinants and ro ots of unity of prime order, Proc. Amer. Math. Soc., 58 (1976) 51-54.

[14] P. E. Frenkel, Simple proof of Chebotarev's theorem on ro ots of unity, http://arxiv.org/abs/0312398.

[15] GAP Groups, Algorithms and Programming, www.gap-system.org

[16] R. G. Gallager, Low Density Parity Check Co des, IRE Trans., 8 (1962) 21-28.

[17] D. Goldstein, R. M. Guralnick and I. M. Isaacs, Inequalities for nite group p ermutation mo dules, Trans. Amer. Math. Soc., 357 no. 10 (2005) 4017-4042.

[18] D. Hamlet, Science, Mathematics, Computer Science, Software Engineering, The Computer Journal, 55 no. 1 (2012) 99-110, (doi:10.1093/comjnl/bxr090).

[19] W. C. Huffman, V. S. Pless and R. A. Brualdi, Handbook of Coding Theory, 1,2, North-Holland, Amsterdam, 1998.

[20] P. Hurley and T. Hurley, Co des from zero-divisors and units in group rings, Int. J. Inf. Coding Theory, 1 no. 1 (2009) 57-87.

[21] P. Hurley and T. Hurley, Block co des from matrix and group rings, Chapter 5, in Selected Topics in Information and Coding Theory , eds. I. Woungang, S. Misra, S.C. Misma, World Scientic, 2010 159-194.

[22] P. Hurley and T. Hurley, LDPC and convolutional co des codes from matrix and group rings, Chapter 6, in Selected Topics in Information and Coding Theory, eds. I. Woungang, S. Misra, S. C. Misma, World Scientic, 2010 195-238.

[23] T. Hurley, Group rings and rings of matrices, Int. J. Pure Appl. Math., 31 no. 3 (2006) 319-335.

[24] T. Hurley, Convolutional co des from units in matrix and group rings, Int. J. Pure Appl. Math., 50 no. 3 (2009) 431-463.

[25] T. Hurley, Self-dual and dual-containing co des using group rings, http://arxiv.org/abs/0711.3983.

[26] B. Hurley and Ted Hurley, Paraunitary matrices and group rings, Int. J. Group Theory, 3 no. 1 (2014) 31-56, http://arxiv.org/abs/1205.0703.

[27] B. Hurley and T. Hurley, Group ring cryptography, Int. J. Pure Appl. Math., 69 no. 1 (2011) 67-86.

[28] B. Hurley and T. Hurley, Systems of MDS co des from units and idemp otents, http://arxiv.org/abs/1301.5596 , 2013.

[29] T. Hurley, Cryptography, key exchange, public key, http://arxiv.org/abs/1305.4063.

[30] T. Hurley, P. McEvoy and J. Wenus, Algebraic constructions of LDPC co des with no short cycles, Int. J. Inf. Coding Theory, 1 no. 3 (2010) 285-297.

[31] R. Johannesson and K. Zigangirov, Fundamentals of Convolutional Coding , IEEE Press, New York, 1999.

[32] D. Kahrobaei, Ch. Koupparis and V. Shpilrain, Public Key Exchange Using Matrices Over Group Rings, Groups Complex. Cryptol, 5 no. 1 (2013) 97-115.

[33] J. Katz and Y. Lindell, Introduction to modern cryptography , Chapman and Hall, Bo ca Raton, 2008.

[34] N. Koblitz, A Course in Number Theory and Cryptography, 114, Springer-Verlag, New York, 1994.

[35] I. Kra and S. Simanca, On circulant matrices, Notices Amer. Math. Soc., 59 no. 3 (2012) 368-377.

[36] D. Labate, G. Weiss and E. Wilson, Wavelets, Notices Amer. Math. Soc., 60 no. 1 (2013) 66-76.

[37] D. J. C. MacKay, Information theory, Inference and Learning Algorithms, Cambridge University Press, New York, 2003.

[38] I. McLoughlin and T. Hurley, A Group Ring Construction of the Extended Binary Golay Code, IEEE Trans. Inform. Theory, 54 no. 9 (2008) 4381-4383.

[39] C. Milies and S. Sehgal, An introduction to Group Rings, Klumer, 2002.

[40] J. O'Shaughnessy, Convolutional codes from group rings, Thesis, National University of Ireland Galway, 2011.

[41] J. O'Shaughnessy, Convolutional co des from group rings, to app ear IJICoT (Int. J. Inf. Coding Theory).

[42] J. O'Shaughnessy, `Quick lo ok in' convolutional co des from group rings, preprint.

[43] B. A. Sethuraman, Division Algebras and Wireless Communication, Notices Amer. Math. Soc., 57 no. 11 (2010) 1432-1439.

[44] A. Shokrollahi, B. Hassibi, B. M. Ho chwald and W. Sweldens, Representation theory for high-rate multiple-antenna code design, IEEE Trans. Inform. Theory, 47 no. 6 (2001) 2335-2367.

[45] A. Soman and P. Vaidyanathan, On orthonormal wavelets and paraunitary lterbanks, IEEE Trans. on Signal Processing, 41 no. 3 (1993) 1170-1183.

[46] G. Strang and T. Nguyen, Wavelet and Filter Banks, Wellesley-Cambridge Press, 1997.

[47] P. Stevenhagen and H. W. Lenstra Jr., Chebotarev and his density theorem, Math. Intel l., 18 (1996) 26-37.

[48] T. Tao, An uncertainty principle for cyclic groups of prime order, Math. Res. Lett., 12 no. 1 (2005) 121-127.

[49] T. T. blog, http://terrytao.wordpress.com/2007/04/13/compressed-sensing-and-single-pixel-cameras.

[50] P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice-Hall, 1993.