Abstract
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 Fp, where p is an odd prime number. The results which we want to discuss are due to G. van der Geer and F. Hirzebruch [36, pp. 759-798]. In Sect. 1.3 we associated an integral lattice in Rn to a binary linear code of length n. In Sect. 5.2 we shall generalize this construction by associating a lattice over the integers of a cyclotomic field to a linear code over Fp. In this section we shall study lattices over integers of cyclotomic fields. For the background on algebraic number theory see also [76] and [87].
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© 2013 Springer Fachmedien Wiesbaden
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Ebeling, W. (2013). Lattices over Integers of Number Fields and Self-Dual Codes. In: Lattices and Codes. Advanced Lectures in Mathematics. Springer Spektrum, Wiesbaden. https://doi.org/10.1007/978-3-658-00360-9_5
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DOI: https://doi.org/10.1007/978-3-658-00360-9_5
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