Steven T. Dougherty

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In this paper, we study self-dual codes over the ring Z 2k of the integers modulo 2k with relationships to even unimodular lattices, modular forms, and invariant rings of 1 nite groups. We introduce Type II codes over Z 2k which are closely related to even unimodular lattices, as a remarkable class of self-dual codes and a generalization of binary Type II(More)
We study self-dual codes over the rings Z8 and Z9. We define various weights and weight enumerators over these rings and describe the groups of invariants for each weight enumerator over the rings. We examine the torsion codes over these rings to describe the structure of self-dual codes. Finally we classify self-dual codes of small lengths over Z8.
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings Rk. We give a linear programming bound on the largest size of an LCD code of given length and minimum distance. We make a table(More)