Isodual Codes over \Bbb Z 2 k and Isodual Lattices
Christine Bachoc
, T.Aaron Gulliver
and Masaaki Harada
DOI: 10.1023/A:1011259823212
Abstract
A code is called isodual if it is equivalent to its dual code, and a lattice is called isodual if it is isometric to its dual lattice. In this note, we investigate isodual codes over 
2 k . These codes give rise to isodual lattices; in particular, we construct a 22-dimensional isodual lattice with minimum norm 3 and kissing number 2464.
2 k . These codes give rise to isodual lattices; in particular, we construct a 22-dimensional isodual lattice with minimum norm 3 and kissing number 2464.Pages: 223–240
Keywords: isodual lattices; isodual codes over $Zopf_{ k }$ and double circulant codes
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References
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2. A. Bonnecaze, A.R. Calderbank, and P. Solé, “Quaternary quadratic residue codes and unimodular lattices,” IEEE Trans. Inform. Theory 41 (1995), 366-377.
3. J.H. Conway and N.J.A. Sloane, Sphere Packing, Lattices and Groups (2nd ed.), Springer-Verlag, New York, 1993.
4. J.H. Conway and N.J.A. Sloane, “A new upper bound on the minimal distance of self-dual codes,” IEEE Trans. Inform. Theory 36 (1990), 1319-1333.
5. J.H. Conway and N.J.A. Sloane, “On lattices equivalent to their duals,” J. Number. Theory 48 (1994), 373-382.
6. T.A. Gulliver and M. Harada, “Extremal Type II double circulant codes over Z4 and construction of 5- (24, 10, 36) designs,” Discrete Math. 194 (1999), 129-137.
7. T.A. Gulliver and M. Harada, “Double circulant self-dual codes over Z2k ,” IEEE Trans. Inform. Theory 44 (1998), 3105-3123.
8. G.T. Kennedy and V. Pless, “On designs and formally self-dual codes,” Des. Codes and Cryptogr. 4 (1994), 43-55.
9. H.-G. Quebbemann, “Modular lattices in Euclidean spaces,” J. Number. Theory 54 (1995), 190-202.
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