Geodesic
Representations of Lie Algebras and Coding Theory
Xiaoping Xu1
1Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, P. R. China
Journal of Lie Theory, Tome 22 (2012) no. 3, pp. 647-682

Voir la notice de l'article provenant de la source Heldermann Verlag

We present a connection between binary and ternary orthogonal codes and finite-dimensional modules of simple Lie algebras. The Weyl groups of the Lie algebras are symmetries of the related codes. It turns out that certain weight matrices of sl(n,C) and o(2n,C) generate doubly-even binary orthogonal codes and ternary orthogonal codes with large minimal distances. Moreover, we prove that the weight matrices of F4, E6, E7 and E8 on their minimal irreducible modules and adjoint modules all generate ternary orthogonal codes with large minimal distances. In determining the minimal distances, we have used the Weyl groups and branch rules of the irreducible representations of the related simple Lie algebras.
Classification : 17B10, 94B60, 17B25
Mots-clés : Simple Lie algebra, irreducible module, weight matrix, orthogonal code, minimal weight of a code

Xiaoping Xu  1

1 Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, P. R. China 
Xiaoping Xu. Representations of Lie Algebras and Coding Theory. Journal of Lie Theory, Tome 22 (2012) no. 3, pp. 647-682. http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a1/
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     title = {Representations of {Lie} {Algebras} and {Coding} {Theory}},
     journal = {Journal of Lie Theory},
     pages = {647--682},
     year = {2012},
     volume = {22},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2012_22_3_a1/}
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