R. Scharlau and R. Schulze-Pillot, Extremal Lattices, in Algorithmic Algebra and Number Theory, edited by B.H. Matzat, G.-M. Greuel, G. Hiss, Springer Verlag 1999. 19  Home/Search Document Details and Download
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Isodual Codes over Z_2k and Isodual Lattices - Bachoc, Gulliver (Correct)
....k = 2; 3 for each dimension 2n. In Table 3, we list (2n) for 10 2n 24, and the third column gives the double circulant code which provides (2n) The fourth and fth columns list the highest minimum norms K (2n) and U (2n) among known isodual lattices and unimodular lattices, from [5] [11] and [3] respectively. Note that information on the highest minimum 8 norm among isodual lattices in dimensions 17 to 22 is lacking in [5] In that range of dimensions, the best known isodual lattices are in the family of modular lattices of level l. If such a lattice has minimum norm , then ....
....isodual lattices in dimensions 17 to 22 is lacking in [5] In that range of dimensions, the best known isodual lattices are in the family of modular lattices of level l. If such a lattice has minimum norm , then the corresponding idodual one has minimum norm = p l. We refer to the survey [11] for information on lattices with parameters: n; l; 12; 3; 4) 14; 3; 4) 16; 2; 4) 18; 3; 4) 20; 7; 8) in lattice Table 3: The Minimum Norm for Isodual Lattices from Double Circulant Codes Dimension 2n (2n) Code K (2n) U (2n) 10 2 D 4;10 2 1 12 2 D 6;12 p 16=3 2 14 2 D 4;14 ; ....
R. Scharlau and R. Schulze-Pillot, Extremal Lattices, in Algorithmic Algebra and Number Theory, edited by B.H. Matzat, G.-M. Greuel, G. Hiss, Springer Verlag 1999. 19
Classification of Hermitian Forms With the Neighbour Method - Schiemann (1998) (1 citation) (Correct)
....are spaces of modular forms where we have a unique extremal form f(z) 1 P mk e 2 imz with maximal k 1 among such modular forms. This holds for l 1 j 24. Lattices whose theta series are extremal modular forms are called (analytically) extremal. For a survey on extremal lattices see [SSP]. Let E = Q Gamma p Gammal Delta for a squarefree l 0. Unimodular hermitian lattices L in a hermitian space (E n ; h) are l modular lattices in the quadratic space (E n ; t) over Q, where t : 1=2 tr E=Q ffih if l j 2; 3 (mod 4) or t : tr E=Q ffih if l j 1 (mod 4) respectively. ....
Rudolf Scharlau and Rainer Schulze-Pillot. Extremal lattices. to appear.
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