17 research outputs found
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
Upper bounds on cyclotomic numbers
In this article, we give upper bounds for cyclotomic numbers of order e over
a finite field with q elements, where e is a divisor of q-1. In particular, we
show that under certain assumptions, cyclotomic numbers are at most
, and the cyclotomic number (0,0) is at most
, where k=(q-1)/e. These results are obtained by
using a known formula for the determinant of a matrix whose entries are
binomial coefficients.Comment: 11 pages, minor revisio
Special Self-Dual Codes over (Theory and Applications of Combinatorial Designs with Related Field)
Classification of Type II code over GF(4) of some small lengths (Codes, lattices, vertex operator algebras and finite groups)
and
A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F 2 f. We show how to construct Jacobi forms with various index over the totally real field. This is one of extension of Broué-Enguehard map