Bibliography of maximal determinants

References

[Ba] G. Barba, Intorno al teorema di Hadamard sui determinanti a valore massimo, Giorn. Mat. Battaglini 71 (1933) 70-86.
[Bau] L. D. Baumert, Hadamard matrices of orders 116 and 232, Bull. Amer. Math. Soc. 72 (1966) 237.
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[Be] M. R. Best, The excess of a Hadamard matrix, Indag. Math. 39 (1977) 357-361.
[Bh] K. N. Bhattacharya, On a new symmetrical balanced incomplete block design, Bull. Calcutta Math. Soc. 36 (1944) 91-96.
[BFW] I. Bouyukliev, V. Fack, and J. Winne, Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes, in European Conference on Combinatorics, Graph Theory and Applications 2005, volume AE of DMTCS Proceedings, Sefan Felsner, Ed., Discrete Mathematics and Theoretical Computer Science (2005) 93-98.
[BOOZ] R. P. Brent, W. P. Orrick, J. Osborn, and P. Zimmermann, Maximal determinants and saturated D-optimal designs of orders 19 and 37, (preprint, 2011) http://arxiv.org/abs/1112.4160.
[Br] A. E. Brouwer, An infinite series of symmetric designs, Math. Centrum Amsterdam Report ZW 202/83 (1983).
[BHH] W. G. Bridges, M. Hall, Jr. and J. L. Hayden, Codes and designs, J. Combin. Theory Ser. A 31 (1981) 155-174.
[Ca] P. J. Cameron, Hadamard matrices, Encyclopedia of Design Theory.
[C1] J. H. E. Cohn, On determinants with elements ±1, II, Bull. London Math. Soc. 21 (1989) 36-42.
[C2] J. H. E. Cohn, A D-optimal design of order 102, Discrete Math. 102 (1992) 61-65.
[C3] J. H. E. Cohn, On the number of D-optimal designs, J. Combin. Theory Ser. A 66 (1994) 214-225.
[C4] J. H. E. Cohn, Almost D-optimal designs, Utilitas Math. 57 (2000) 121-128.
[CD] C. J. Colbourn and J. H. Dinitz, The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton, 1996.
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[CK] Th. Chadjipantelis and S. Kounias, Supplementary difference sets and D-optimal designs for n≡2 mod 4, Discrete Math. 57 (1985) 211-216.
[CKM1] T. Chadjipantelis, S. Kounias and C. Moyssiadis, Construction of D-optimal designs for n≡2 mod 4 using block-circulant matrices, J. Combin. Theory Ser. A 40 (1985) 125-135.
[CKM2] T. Chadjipantelis, S. Kounias and C. Moyssiadis, The maximum determinant of 21×21 (+1, -1)-matrices and D-optimal designs, J. Statist. Plann. Inference 16 (1987) 167-178.
[De] R. H. F. Denniston, Enumeration of symmetric designs (25, 9, 3), in Algebraic and Geometric Combinatorics, E. Mendelsohn, Ed., North-Holland Math. Stud. 65 Annals of Discrete Mathematics, 15 (1982) 111-127.
[D1] D. Z. Djokovic, On maximal (1, -1)-matrices of order 2n, n odd, Radovi Matematicki 7 (1991) 371-378.
[D2] D. Z. Djokovic, Some new D-optimal designs, Australas. J. Combin. 15 (1997) 221-231.
[DK] D. Z. Djokovic and I. S. Kotsireas, New results on D-optimal designs, J. Combin. Designs 20 (2012) 278-289.
[DNST] R. Dowdeswell, M. Neubauer, B. Solomon and K. Tumer, Binary Matrices of Maximal Determinant, http://www.imrryr.org/~elric/matrix/.
[E1] H. Ehlich, Determinantenabschätzungen für binäre Matrizen, Math. Z. 83 (1964) 123-132.
[E2] H. Ehlich, Determinantenabschätzungen für binäre Matrizen mit N≡3 mod 4, Math. Z. 84 (1964) 438-447.
[EZ] H. Ehlich and K. Zeller, Binäre Matrizen, Z. Angew. Math. Mech. 42 (1962) T20-T21.
[EM] H. Enomoto and M. Miyamoto, On maximal weights of Hadamard matrices, J. Combin. Theory Ser. A 29 (1980) 94-100.
[FK] N. Farmakis and S. Kounias, The excess of Hadamard matrices and optimal designs, Discrete Math. 67 (1987) 165-176.
[FS] R. J. Fletcher and J. Seberry, New D-optimal designs of order 110, Australas. J. Combin. 23 (2001) 49-52.
[FKS] R. J. Fletcher C. Koukouvinos, and J. Seberry, New skew-Hadamard matrices of order 4.59 and new D-optimal designs of order 2.59, (preprint 2003, submitted.)
[GK] Z. Galil and J. Kiefer, D-optimum weighing designs, Ann. Statist. 8 (1980) 1293-1306.
[GS] J. M. Goethals and J. J. Seidel, Strongly regular graphs derived from combinatorial designs, Can. J. Math. 22 (1970) 597-614.
[Gys] M. Gysin, New D-optimal designs via cyclotomy and generalised cyclotomy, Australas. J. Combin. 15 (1997) 247-255.
[Had] J. Hadamard, Résolution d'une question relative aux déterminants, Bull. Sci. Math. 17 (1893) 240-246.
[Hal] M. Hall, Jr., Hadamard matrices of order 20, Technical Report 32-761, Jet Propulsion Lab., Pasadena, CA (1965).
[HK] W. H. Holzmann and H. Kharaghani, A D-optimal design of order 150, Discrete Math. 190 (1998) 265-269.
[Hu] Q. M. Husain, On the totality of the solutions for the symmetrical incomplete block designs: λ=2, k=5 or 6, Sankhya 7 (1945) 204-208.
[ILL] N. Ito, J. S. Leon and J. Q. Longyear, Classification of 3-(24, 12, 5) designs and 24-dimensional Hadamard matrices, J. Combin. Theory Ser. A 31 (1981) 66-93.
[Kh] H. Kharaghani, A construction of D-optimal designs for N≡2 mod 4, J. Combin. Theory Ser. A 46 (1987) 156-158.
[K1] H. Kimura, New Hadamard matrix of order 24, Graphs Combin. 5 (1989) 235-242.
[K2] H. Kimura, Classification of Hadamard matrices of order 28 with Hall sets, Discrete Math. 128 (1994) 257-268.
[K3] H. Kimura, Classification of Hadamard matrices of order 28, Discrete Math. 133 (1994) 171-180.
[KKS] C. Koukouvinos, S. Kounias and J. Seberry, Supplementary difference sets and optimal designs, Discrete Math. 88 (1991) 49-58.
[KMS] C. Koukouvinos, M. Mitrouli and J. Seberry, Bounds on the maximum determinant for (1, -1) matrices, Bull. Inst. Combin. Appl. 29 (2000) 39-48.
[KF] S. Kounias and N. Farmakis, On the excess of Hadamard matrices, Discrete Math. 68 (1988) 59-69.
[KKNK1] S. Kounias, C. Koukouvinos, N. Nikolaou and A. Kakos, The non-equivalent circulant D-optimal designs for n≡2 mod 4, n≤54, n=66, J. Combin. Theory Ser. A 65 (1994) 26-38.
[KKNK2] S. Kounias, C. Koukouvinos, N. Nikolaou and A. Kakos, The non-equivalent circulant D-optimal designs for n=90, J. Statist. Plann. Inference 53 (1996) 253-259.
[M1] N. Metropolis, Spectra of determinant values in (0, 1) matrices. In A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory: Proceedings of the Science Research Atlas Symposium No. 2 held at Oxford, from 18-23 August, 1969, pages 271–276, London, 1971. Academic Press.
[M] A. M. Mood, On Hotelling's weighing problem, Ann. Math. Stat. 17 (1946) 432-446.
[MK] C. Moyssiadis and S. Kounias, The exact D-optimal first order saturated design with 17 observations, J. Statist. Plann. Inference 7 (1982) 13-27.
[O1] W. P. Orrick, The maximal {-1, 1}-determinant of order 15, (accepted for publication in Metrika) http://arxiv.org/abs/math.CO/0401179.
[O2] W. P. Orrick, Switching operations for Hadamard matrices, (preprint, 2005) http://arxiv.org/abs/math.CO/0507515.
[O3] W. P. Orrick, On the enumeration of some D-optimal designs, (preprint, 2005) http://arxiv.org/abs/math.CO/0511141.
[OS] W. P. Orrick and B. Solomon, Large determinant sign matrices of order 4k+1, (preprint, 2003, submitted) http://arxiv.org/abs/math.CO/0311292
[OSDS] W. P. Orrick, B. Solomon, R. Dowdeswell, and W. D. Smith, New lower bounds for the maximal determinant problem, (preprint, 2003) http://arxiv.org/abs/math.CO/0304410.
[P] R. E. A. C. Paley, On orthogonal matrices, J. Math. Phys. 12 (1933) 311-320.
[PS1] M.-O. Pavcevic and E. Spence, Some new symmetric designs with λ=10 having an automorphism of order 5, Discrete Math. 196 (1999) 257-266.
[PS2] M.-O. Pavcevic and E. Spence, Some new symmetric designs, J. Combin. Designs 7 (1999) 426-430.
[R] D. Raghavarao, Some optimum weighing designs, Ann. Math. Statist. 30 (1959) 295-303.
[SS] Y. S. Sathe and R. G. Shenoy, Construction of maximal weight Hadamard matrices of order 48 and 80, ARS Combin. 19 (1985) 25-35.
[Sa] K. Sawade, A Hadamard matrix of order 268, Graphs Combin. 1 (1985) 185-187.
[Sc1] U. Scarpis, Sui Determinants di Valore Massimo, Rendiconti della Reale Istituto Lombardo di Scienze e Lettere, Serie II 31 (1898) 1441-1446.
[Sc] K. W. Schmidt, Problem 72-19, A bound for a 4^k-order maximal (0, 1) determinant, SIAM Rev. 15 (1973) 673-674.
[Sl] N. J. A. Sloane, editor (2002), The On-Line Encyclopedia of Integer Sequences, published electronically at http://oeis.org/.
[Sm] Warren D. Smith, Studies in Computational Geometry Motivated by Mesh Generation, Ph. D. dissertation, Princeton University (1988).
[Sp1] E. Spence, Skew-Hadamard matrices of the Goethals-Seidel type, Canad. J. Math. 27 (1975) 555-560.
[Sp2] E. Spence, Symmetric (41, 16, 6)-designs with a nontrivial automorphism of odd order, J. Combin. Designs 1 (1993) 193-211.
[Sp3] E. Spence, Five nondual 2-(41, 16, 6) designs with a trivial automorphism group, Ars Combin. 41 (1995) 117-122.
[Sp4] E. Spence, Regular two-graphs on 36 vertices, Lin. Alg. Appl. 226-228 (1995) 459-497.
[SY] J. Seberry and M. Yamada, Hadamard matrices, sequences, and block designs, in Contemporary design theory, J. H. Dinitz and J. R. Stinson, eds., Wiley-Intersci. Ser. Discrete Math. Optim., Wiley, New York, 1992, 431-560.
[Sy] J. J. Sylvester, Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tesselated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers, London Edinburgh and Dublin Philos. Mag. and J. Sci. 34 (1867) 461-475.
[T] J. A. Todd, A combinatorial problem, J. Math. Phys. 12 (1933) 321-333.
[To] S. Topalova, Classification of Hadamard matrices of order 44 with automorphisms of order 7, Discrete Math. 260 (2003) 275-283.
[vT] T. van Trung, The existence of symmetric block designs with parameters (41, 16, 6) and (66, 26, 10), J. Combin. Theory Ser. A 33 (1982) 201-204.
[WSW] W. D. Wallis, Anne Penfold Street, and Jennifer Seberry Wallis, Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices, Springer-Verlag, Berlin 1972.
[Wi] J. Williamson, Determinants whose elements are 0 and 1, Amer. Math. Monthly 53 (1946) 427-434.
[Wo] M. Wojtas, On Hadamard's inequality for the determinants of order non-divisible by 4, Colloq. Math. 12 (1964) 73-83.
[Y1] C. H. Yang, Some designs for maximal (+1, -1)-determinant of order n≡2 (mod 4), Math. Comp. 20 (1966) 147-148.
[Y2] C. H. Yang, A construction for maximal (+1, -1)-matrix of order 54, Bull. Amer. Math. Soc. 72 (1966) 293.
[Y3] C. H. Yang, On designs of maximal (+1, -1)-matrices of order n≡2 (mod 4), Math. Comp. 22 (1968) 174-180.
[Y4] C. H. Yang, On designs of maximal (+1, -1)-matrices of order n≡2 (mod 4), II, Math. Comp. 23 (1969) 201-205.
[Y5] C. H. Yang, Maximal binary matrices and sum of two squares, Math. Comp. 30 (1976) 148-153.

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Last modified 17 October 2012.
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