Group Codes On Deligne-Lusztig Varieties
Johan P. Hansen · 2005
We construct algebraic geometric error-correcting codes using the Deligne-Lusztig varieties [1] associated to a connected reductive algebraic group G defined over a finite field Fq, with Frobenius map f. The codes are obtained as geometric Goppa codes [2], that is linear error-correcting codes constructed from algebraic varieties. The finite group GF of Lie type acts as Fq -rational automorphisms on the codes and they become modules over the group algebra Fq [GF]The Deligne-Lusztig varieties used in the construction of the codes have in some cases many Fq -rational points, which ensures that the codes have a large word length.