Lattices over Integers of Number Fields and Self-Dual Codes
Wolfgang Ebeling · Advanced lectures in mathematics · 2002
Up to now, we have only considered binary codes. In this chapter we want to present a generalization of the results of Chapter 2 to self-dual codes over 𝔽 p , where p is an odd prime number. The results which we want to discuss are due to G. van der Geer and F. Hirzebruch [Hir87, pp. 759–798]. In §1.3 we associated an integral lattice in ℝ n to a binary code of length n . In §5.2 we shall generalize this construction by associating a lattice over the integers of a cyclotomic field to a code over 𝔽 p . In this section we shall study lattices over integers of cyclotomic fields. For the background on algebraic number theory see also [Sam67] and [ST87]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.