Publications by Patrick Fitzpatrick

Papers in journals and refereed proceedings

1.      P. Fitzpatrick and J. Wiegold, Embedding group amalgams, Bull. Austral. Math. Soc. 24 (1981), 373-79.

2.      P. Fitzpatrick and L.G. Kovács, Varieties of nilpotent groups of class four I, J. Austral. Math. Soc., Ser. A 35 (1983), 59-73.

3.      P. Fitzpatrick, Varieties of nilpotent groups of class four II, J. Austral. Math. Soc., Ser. A (1983), 74-108.

4.      P. Fitzpatrick, Varieties of nilpotent groups of class four III, J. Austral. Math. Soc., Ser. A (1983), 109-122.

5.      P. Fitzpatrick, Order conjugacy in finite groups, Proc. Roy. Ir. Acad. 85A (1985), 53-58.

6.      P. Fitzpatrick, Groups in which an automorphism inverts precisely half the elements, Proc. Roy. Ir. Acad. 86A, (1986), 81-89.

7.      P. Fitzpatrick and G.H. Norton, Linear recurrence relations and an extended subresultant algorithm, Lecture Notes in Computer Science, 208 (1988), 233-243.

8.      P. Fitzpatrick and G.H. Norton, Finding a basis for the characteristic ideal of an n-dimensional linear recurring sequence, IEEE Trans. Information Theory, IT-36 (1990), 1480-1487.

9.      P. Fitzpatrick and G.H. Norton, Linear recurring sequences and the path weight enumerator of a convolutional code Elect. Lett., 27 (1991), 98-99.

10.  P. Fitzpatrick and C.C. Murphy, Fault tolerant matrix triangularization and the solution of linear systems of equations, in Proc. Conf. on Application Specific Array Processors, Berkeley, Calif. Aug. 1992, 469-480.

11.  P. Fitzpatrick and J. Flynn, A Gröbner basis technique for Padé approximation. J. Symbolic Computation, 13 (1992), 133-138.

12.  P. Fitzpatrick and C.C. Murphy, Solution of linear systems of equations in the presence of two transient hardware faults. IEE Proc.-E, Computers and Digital Techniques, 140 (1993), 247-257.

13.  P. Fitzpatrick, New time domain errors and erasures decoding algorithm for BCH codes. Elect. Lett., 30:2 (1994), 110-111.

14.  P. Fitzpatrick, A coding theoretic approach to fault tolerant matrix decompositions and solution of linear systems of equations, in Mathematics in Signal Processing III, J.G. McWhirter (Ed.)}, Clarendon Press, Oxford, 1994, 41-50.

15.  P. Fitzpatrick, On fault tolerant matrix decomposition, J. VLSI Sig. Proc., 8 (1994), 1-11.

16.  P. Fitzpatrick, Decoding BCH codes by canonical choice in F [x] x F[x], in Codes and Cyphers, (P.G. Farrell, ed.), Formara Ltd., Southend-on-Sea, UK, 1994, 195-204.

17.  M.P. Connolly and P. Fitzpatrick, Fault tolerant QR decomposition for adaptive signal processing, in Proc. SPIE Advanced Signal Processing: Algorithms, Architectures, and Implementations V, San Diego, July 1994, 740-750.

18.  P. Fitzpatrick, On fault tolerant matrix decomposition. J. VLSI Signal Processing, 8 (1994), 1-11.

19.  P. Fitzpatrick, Error correcting codes: at the forefront of applied abstract algebra. Bull. Inst. Math. and its Appls. 30:9-10 (1994), 138-143.

20.  P. Fitzpatrick and G.H. Norton, The Berlekamp-Massey algorithm and linear recurring sequences over a factorial domain. Applicable Algebra in Engineering, Communication and Computing, 6 no. 4/5 (1995) 309-323.

21.  P. Fitzpatrick, On the key equation. IEEE Transactions on Information Theory, 41, no. 5 (1995), 1290-1302.

22.  P. Fitzpatrick, Fault tolerant linear algebra. Bull. Inst. Math. Appls, 32, no. 1/2 (1996) 17-22.

23.  M. P. Connolly and P. Fitzpatrick, Fault tolerant QRD recursive least squares. IEE Proc.-E, Computers and Digital Techniques, 143 (1996), 137-144.

24.  P. Fitzpatrick, Extending backward error assertions to tolerance of large errors in floating point computations, IEEE Trans. on Computers, 46 (1997), 505-510.

25.  P. Fitzpatrick, Solving a multivariable congruence by change of term order , J. Symb. Comp., 24 (1997) 575-589.

26.  P. Fitzpatrick, On the scalar rational interpolation problem , Math. of Control, Signals, and Systems, 9 (1996), 352-369.P. Fitzpatrick, Rational approximation using Grobner bases: some numerical results, Proc. Mathematics in Signal Processing IV , J.G McWhirter and I.K Proudler, eds, IMA (UK) Conference Series 67, 1998, 35-46.

27.  M.P. Connolly and P. Fitzpatrick, Fault tolerant Faddeeva algorithm , J. Par. Dist. Comp. , 53 (1998), 78-89.

28.  P. Fitzpatrick and S.M. Jennings, Comparison of two algorithms for decoding alternant codes , Appl. Alg. in Eng. Comm., and Comp., 9 (1998), 211-220.

29.  E. M. Popovici and P. Fitzpatrick, New division algorithm over GF(2 m), Elect. Lett. , 34 No. 19 (1998) 1843-1844.

30.  P. Fitzpatrick, Errors and erasures decoding of BCH codes , IEEE Proc. E , IEE Proc.-Commun. , 146 No. 2 (1999) 79-81.

31.  K. Lally, P. Fitzpatrick, Algebraic structure of quasicyclic codes, Disc. Appl. Math., 111 (2001) 157-175.

32.  H. O'Keeffe, P. Fitzpatrick, Recursive construction of Gr\"obner bases for the solution of polynomial congruences, IMA Proc. Codes and Graphical Models, B. Marcus and J. Rosenthal, eds. (Vol. 123 in IMA Mathematics and its Applications), 2000,  299-311.

33.  E. Byrne, P. Fitzpatrick, Gröbner bases over Galois rings with an application to decoding, J. Symb. Comp., 31 (2001) 565-584.

34.  P. Fitzpatrick, J.A. Ryan, Counting irreducible Goppa codes, J. Austral. Math. Soc., 71(3) (2001) 299-306.

35.  E. Byrne, P. Fitzpatrick, Hamming metric decoding of alternant codes over Galois rings, IEEE Trans. on Inform. Thy, IT-48 (2002) 683-694 .

36.  H. O'Keeffe, P. Fitzpatrick, Gröbner basis solution of constrained interpolation problemsLin. Alg. Appls., 351-352 (2002) 533-551.

37.  E. Popovici, P. Fitzpatrick, Algorithm and architecture for a multiplicative Galois field processor, IEEE Trans. Inform. Thy, 49 (2003), 3303-3307.

38.  C. Wolf, P. Fitzpatrick, Direct division in factor rings, Elect. Lett. 38 No. 21 (2002) 1253-1254.

39.  P. Fitzpatrick, J.A. Ryan, Enumeration of irreducible Goppa codes, Discrete Applied Mathematics, 154(2) (2005) 399-412

40. K. O'Brien, P. Fitzpatrick, Improving the Varshamov bound by counting components in the Varshamov graph, to appear in Designs, Codes, and Cryptography.

41.  H. O’Keeffe and P. Fitzpatrick, Hard and soft-decision list decoding of AG codes using Gröbner basis solutions to constrained interpolations, submitted to J. Symbolic Computation .

 

Selected conference papers, reviews, and short communications

1.      The impossible scores problem by modular arithmetic, Math. Gaz., 1976, 219-220.

2.      Invited review, The Cockcroft Report, Ir. Math. Soc. Newsletter  5, 1982, 35-40.

3.      Invited review, Combinatorics on words, by M. Lothaire, Ir. Math. Soc. Newsletter 9, 1983, 67-71

4.      Generating and enumerating magic squares, Math. Gaz. 69, 1985, 259-261.

5.      CAYLEY-group theory by computer, Ir. Math. Soc. Bull. 16, 1986, 56-63.

6.      Asymmetric cryptography, Ir. Math. Soc. Bull. 20, 1988, 21-31.

7.      Comparison of certain coding schemes for error correction, Data Communications Technology, NIHE, Limerick, 1988, 502-508 (with R. Bennis).

8.      A systolic version of the extended Euclidean algorithm, Systolic Array Processors, Killarney, 1989, 477-486 (with J. Nelson and G.H. Norton).

9.      An improved systolic extended Euclidean algorithm for RS decoding, Application Specific Array Processors, Princeton, 1990, 448-456 (with R. Doyle and J. Nelson).

10.  Linear recurring sequences and the path weight enumerator of a convolutional code, Int. Symp. Inform. Thy, Budapest, 1991, 199 (with.G.H. Norton).

11.  Fault tolerant matrix triangularization and the solution of linear systems of equations, Application Specific Array Processors, Berkeley, 1992, 469-480 (with C.C. Murphy).

12.  A new look at the key equation, Int. Symp. Inform. Theory, San Antonio (1993), 98.

13.  Comparison of two algorithms for decoding BCH codes, Int. Symp. Inform. Theory, Ulm, 1997, 325 (with S.M. Jennings).

14.  Invited Review, Introduction to Coding Theory by J.H van Lint, Ir. Math. Soc. Bull. 38, 1997,   69-76.

15.  Invited Review, MAPLE: A Comprehensive Introduction by R. Nicolaides and N. Walkington, Siam Review 39, 1997, 792-793.

16.  Construction and classification of quasicyclic codes, Int. Workshop on Coding and Cryptography, WCC1999, Paris, 1999, 11-20 (with K. Lally).

17.  Recursive construction of Gröbner bases for the solution of polynomial congruences, IMA Codes and Graphical Models, Minneapolis, 1999, 299-310 (with H. O’Keeffe).

18.  FPGA design trade-offs for solving the key equation in Reed-Solomon decoding, 9th Field Programmable Logic and Appls, FPL'99, Strathclyde, 1999, LNCS 1673, 353-358 (with C.C. Murphy and E. Popovici).

19.  Invited Review, The Mathematica Primer by K.R. Coombes et al, Siam Review, 41, No. 4, 1999, 834-835.

20.  Invited Review, Algèbre Discrète et Codes Correcteurs by O. Papini and J. Wolfmann, Math. Reviews, 2000.

21.  Gröbner bases and alternant codes over Galois rings, Int. Symp. Inform. Theory, Sorrento, 2000 (with E. Byrne).

22.  Algebraic structure of quasicyclic codes, Int. Symp. Inform. Theory, Sorrento, 2000 (with K. Lally).

23.  Implementation of a Hermitian decoder, Int. Symp. Inform. Theory, Washington DC, 2001 (with E. Popovici, M, O’Sullivan, and R. Kötter).

24.  The number of inequivalent irreducible Goppa codes, Int. Workshop on Coding and Cryptography, WCC2001, Paris, 2001 (with J.A. Ryan).

25.  VLSI design of a Galois field arithmetic processor, 23rd Int. Conf. on Microelect., Nis, Yugoslavia, May 2002 (with E. Popovici).

26.  Hard and soft-decision list decoding of AG codes using Gröbner basis solutions to constrained interpolations, Int. Symp. Inform. Theory, Lausanne, 2002 (with H. O’Keeffe).

27.  Irreducible Goppa codes, Int. Workshop on Coding and Cryptography, WCC2003, Paris, 2003 407-416 (with J.A. Ryan).

28.  Enumeration of irreducible Goppa codes, Int. Symp. on Inform. Thy, Chicago, 2004 (with J.A. Ryan).

29.  Improving the Varshamov bound by counting components in the Varshamov graph, Int. Symp. on Inform. Thy, Chicago, 2004 (with K. O’Brien).