Geodesic
Polynomial Invariants of Finite Linear Groups of Degree Two
Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 317-330

Voir la notice de l'article provenant de la source Cambridge University Press

Recently invariant theory of linear groups has been used to determine the structure of several weight enumerators of codes. Under certain conditions on the code, the weight enumerator is invariant under a finite group of matrices. Once all the polynomial invariants of this group are known, the form of the weight enumerator is restricted and often useful results about the existence and structure of codes can be found. (See [5], [8], [14], and [15].) Many of the groups in these applications are of degree 2; in this paper all the invariants of finite 2 X 2 matrix groups over C are determined. 
Huffman, W. Cary. Polynomial Invariants of Finite Linear Groups of Degree Two. Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 317-330. doi: 10.4153/CJM-1980-024-6
@article{10_4153_CJM_1980_024_6,
     author = {Huffman, W. Cary},
     title = {Polynomial {Invariants} of {Finite} {Linear} {Groups} of {Degree} {Two}},
     journal = {Canadian journal of mathematics},
     pages = {317--330},
     year = {1980},
     volume = {32},
     number = {2},
     doi = {10.4153/CJM-1980-024-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-024-6/}
}
TY  - JOUR
AU  - Huffman, W. Cary
TI  - Polynomial Invariants of Finite Linear Groups of Degree Two
JO  - Canadian journal of mathematics
PY  - 1980
SP  - 317
EP  - 330
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-024-6/
DO  - 10.4153/CJM-1980-024-6
ID  - 10_4153_CJM_1980_024_6
ER  - 
%0 Journal Article
%A Huffman, W. Cary
%T Polynomial Invariants of Finite Linear Groups of Degree Two
%J Canadian journal of mathematics
%D 1980
%P 317-330
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-024-6/
%R 10.4153/CJM-1980-024-6
%F 10_4153_CJM_1980_024_6

[1] 1. Blichfeldt, H. F., Finite collineation groups (University of Chicago Press, Chicago, 1917). Google Scholar

[2] 2. Burnside, W., Theory of groups of finite order (Dover, New York, 1955). Google Scholar

[3] 3. Coxeter, H. S. M., Regular complex poly topes (Cambridge University Press, 1974). Google Scholar

[4] 4. DuVal, P., Homographies, quaternions and rotations (Oxford: Oxford University Press, 1964). Google Scholar

[5] 5. Gleason, A. M., Weight polynomials of self-dual codes and the MacWilliams identities, in: Actes Congrès Internat. Math. 1970, Vol. 3, Gauthiers-Villars, Paris (1971), 211–215. Google Scholar

[6] 6. Huffman, W. C. and Sloane, N. J. A., Most primitive groups have messy invariants, to appear in Adv. in Math. Google Scholar

[7] 7. Klein, F., Lectures on the icosahedron and the solution of equations of the fifth degree (Dover, New York, 1956). Google Scholar

[8] 8. MacWilliams, F. J., Mallows, C. L., and Sloane, N. J. A., Generalizations of Gleason s theorem on weight enumerators of self-dual codes, IEEE Trans. Information Theory, IT-18 (1972), 794–805. Google Scholar

[9] 9. Mallows, C. L. and Sloane, N. J. A., On the invariants of a linear group of order 336, Proc. Camb. Phil. Soc. 74 (1973), 435–440. Google Scholar

[10] 10. Miller, G. A., Blichfeldt, H. F., and Dickson, L. E., Theory and applications of finite groups (Dover, New York, 1961). Google Scholar

[11] 11. Molien, T., Uber die Invarianten der lineare Substitutionsgruppe, Sitzungsber. Kônig. Preuss. Akad. Wiss. (1897), 1152–1156. Google Scholar

[12] 12. Riemenschneider, O., Die Invarianten der endlichen Untergruppen von GL(2, C), Math Zeit. 153 (1977), 37–50. Google Scholar

[13] 13. Shephard, G. C., and Todd, J. A., Finite unitary reflection groups, Can. J. Math. 6 (1954), 274–304. Google Scholar

[14] 14. Sloane, N. J. A., Error-correcting codes and invariant theory: new applications of a nineteenthcentury technique, Amer. Math. Monthly 84 (1977), 82–107. Google Scholar

[15] 15. Sloane, N. J. A., Weight enumerators of codes, in Combinatorics (Proceedings of the NATO Advanced Study Institute, July, 1974), 115–142. Google Scholar

[16] 16. Stanley, R., Relative invariants of finite groups generated by pseudoreflections, J. Algebra 49 (1977), 134–148. Google Scholar

Cité par Sources :