Geodesic
Combinatorial $S\sb n$-modules as codes
Journal of Algebraic Combinatorics, Tome 4 (1995) no. 1, pp. 47-68.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Certain $\mathbb Z S _{ n}$ mathbbZS_n -modules related to the kernels ofincidence maps between types in the poset defined by the natural productorder on the set of $n$-tuples with entries from 1, frac14 $\ldots , m$ are studied as linear codes (whencoefficients are extended to an arbitrary field $K$). Theirdimensions and minimal weights are computed. The Specht modules areextremal among these submodules. The minimum weight codewords of theSpecht module are shown to be scalar multiples of polytabloids. Ageneralization of t-design arising from the natural permutation $S _{n}$-modules labelled by partitions with $m$parts is introduced. A connection with Reed-Muller codes is noted and acharacteristic free formulation is presented.
Keywords: symmetric group, Specht module, $t$-design, Reed-muller code 
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     author = {Liebler, Robert A. and Zimmermann, Karl-Heinz},
     title = {Combinatorial $S\sb n$-modules as codes},
     journal = {Journal of Algebraic Combinatorics},
     pages = {47--68},
     publisher = {mathdoc},
     volume = {4},
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     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1995__4_1_a1/}
}
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Liebler, Robert A.; Zimmermann, Karl-Heinz. Combinatorial $S\sb n$-modules as codes. Journal of Algebraic Combinatorics, Tome 4 (1995) no. 1, pp. 47-68. http://geodesic.mathdoc.fr/item/JAC_1995__4_1_a1/