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,
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.,
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,
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
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 problems , Lin. 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
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,
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,
10. Linear recurring sequences and the path weight
enumerator of a convolutional code, Int. Symp.
Inform. Thy,
11. Fault tolerant matrix triangularization
and the solution of linear systems of equations, Application Specific Array
Processors,
12. A new look at the key equation, Int. Symp. Inform. Theory,
13. Comparison of two algorithms for decoding BCH
codes, Int. Symp. Inform. Theory,
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
16. Construction and classification of quasicyclic
codes, Int. Workshop on Coding and
Cryptography, WCC1999,
17. Recursive construction of Gröbner bases for the
solution of polynomial congruences, IMA Codes and Graphical Models,
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
19. Invited Review, The Mathematica Primer by K.R. Coombes et al,
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,
22. Algebraic structure of quasicyclic codes, Int. Symp. Inform. Theory,
23. Implementation of a Hermitian decoder, Int. Symp. Inform. Theory,
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.,
26. Hard and soft-decision list decoding of AG codes
using Gröbner basis solutions to constrained interpolations, Int. Symp. Inform. Theory,
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,
29. Improving the Varshamov bound by counting
components in the Varshamov graph, Int. Symp. on Inform. Thy,