6,605 research outputs found
On some new extremal Type II Z4-codes of length 40
Using the building-up method and a modification of the doubling method we construct new extremal Type II Z4-codes of length 40. The constructed codes of type , for ,
are the first examples of extremal Type II Z4-codes of given type and length 40 whose residue codes have minimum weight greater than or equal to 8. Further, we use minimum weight codewords for a construction of 1-designs, some of which are self-orthogonal
Residue codes of extremal Type II Z_4-codes and the moonshine vertex operator algebra
In this paper, we study the residue codes of extremal Type II Z_4-codes of
length 24 and their relations to the famous moonshine vertex operator algebra.
The main result is a complete classification of all residue codes of extremal
Type II Z_4-codes of length 24. Some corresponding results associated to the
moonshine vertex operator algebra are also discussed.Comment: 21 pages, shortened from v
Conference matrices and unimodular lattices
Conference matrices are used to define complex structures on real vector
spaces. Certain lattices in these spaces become modules for rings of quadratic
integers. Multiplication of these lattices by non-principal ideals yields
simple constructions of further lattices including the Leech lattice.Comment: 17 pages. Subitted to European Journal of Combinatoric
On triply even binary codes
A triply even code is a binary linear code in which the weight of every
codeword is divisible by 8. We show how two doubly even codes of lengths m_1
and m_2 can be combined to make a triply even code of length m_1+m_2, and then
prove that every maximal triply even code of length 48 can be obtained by
combining two doubly even codes of length 24 in a certain way. Using this
result, we show that there are exactly 10 maximal triply even codes of length
48 up to equivalence.Comment: 21 pages + appendix of 10 pages. Minor revisio
- …