05864040

j

05864040 Boucher, Delphine Sol\'e, Patrick Ulmer, Felix Skew constacyclic codes over Galois rings. Adv. Math. Commun. 2, No. 3, 273-292 (2008). 2008 Shandong University, Jinan; American Institute of Mathematical Sciences, Springfield, MO EN cyclic codes skew polynomial rings self-dual codes $\Bbb Z_4$-codes modular lattices

doi:10.3934/amc.2008.2.273

Summary: We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over $GR(4, 2)$ are constructed. Euclidean self-dual codes give self-dual $\mathbb Z_4$ - codes. Hermitian self-dual codes yield 3 - modular lattices and quasi-cyclic self-dual $\mathbb Z_4$ - codes.