Abstract
The dimensions of the codes associated to the Ree unital are computed using methods from modular representation theory.
Similar content being viewed by others
References
Char, B.W., Geddes, K.O., Gonnet, G.H., Leong, B.L., Monagan, M.B., and Watt, S.M, “Maple V, Language Reference Manual”, Springer, 1991.
Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., and Wilson, R.A., “Atlas of Finite Groups”, Oxford University Press, 1985.
Feit, W., “The Representation Theory of Finite Groups”, North-Holland Publishing Company, 1982.
Geck, M., “Irreducible Brauer characters of the 3-dimensional special unitary groups in non-defining characteristic”, Comm. Algebra 18 (1990), 563–584.
Hiss, G., “The Brauer trees of the Ree groups”, Comm. Algebra 19 (1991), 871–888.
Klemm, M., “Über den p-Rang von Inzidenzmatrizen”, J. Combin. Theory Ser. A 43 (1986), 138–139.
Landrock, P. and Michler, G.O., “Principal 2-blocks of the simple groups of Ree type”, Trans. Amer. Math. Soc. 260 (1980), 83–111.
Lüneburg, H., “Some remarks concerning the Ree groups of type (G 2)”, J. Algebra 3 (1966), 256–259.
Michler, G.O., “Green correspondence between blocks with cyclic defect groups II”, in: Representations of Algebras, Ottawa 1974, Lecture Notes in Mathematics, 488: 210–235, Springer Verlag, 1975.
Mortimer, B., “The modular permutation representations of the known doubly transitive groups”, Proc. London Math. Soc. (3) 41 (1980), 1–20.
Schönert, M. et al., “GAP — Groups, Algorithms, and Programming”, Lehrstuhl D für Mathematik, RWTH Aachen, Germany, fourth ed., 1994.
Ward, H.N., “On Ree's series of simple groups”, Trans. Amer. Math. Soc. 121 (1966), 62–89.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hiss, G. On the Incidence Matrix of the Ree Unital. Designs, Codes and Cryptography 10, 57–62 (1997). https://doi.org/10.1023/A:1008240303650
Issue Date:
DOI: https://doi.org/10.1023/A:1008240303650