FULLY-DIVERSE LATTICES FROM RAMIFIED CYCLIC EXTENSIONS OF PRIME DEGREE

Abstract

Let p be an odd prime. Algebraic lattices of full diversity in dimension p are obtained from ramified cyclic extensions of degree p. The 3, 5, and 7-dimensional lattices are optimal with respect to sphere packing density and therefore are isometric to laminated lattices in those dimensions. AMS Subject Classification: 11H31, 11R18, 11H50, 94B75