Higher Power Residue Codes and the Leech Lattice
Mehrdad Ahmadzadeh Raji
Department of Mathematical Sciences University of Exeter Exeter EX4 4QE UK
DOI: 10.1007/s10801-005-6279-4
Abstract
We shall consider higher power residue codes over the ring Z 4. We will briefly introduce these codes over Z 4 and then we will find a new construction for the Leech lattice. A similar construction is used to construct some of the other lattices of rank 24.
Pages: 39–53
Keywords: keywords self-dual code; even unimodular lattice; hensel lifting
Full Text: PDF
References
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2. A. Bonnecaze, P. Solé, and A.R. Calderbank, “Quaternary quadratic residue codes and unimodular lattices,” IEEE Trans. Inform. theory 41(2) (1995).
3. R. Chapman, “Higher power residue codes,” Finite Fields Appl. 3 (1997), 353-369.
4. R. Chapman, “Conference matrices and unimodular lattices,” European J. Combin. 22 (2001), 1033-1045.
5. R. Chapman, Personal communication.
6. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 1st edn., Springer Verlag, New York, 1988.
7. R. T. Curtis, “The maximal subgroups of M24,” Math. Proc. Cambridge Philos. Soc. 81 (1977), 185-192.
8. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier Science Publishers, Amsterdam, 1991.
9. J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge University Press, New York, 1992.
10. Zhe-Xian Wan, Quaternary Codes, World Scientific Publishing, London, 1997.