17 research outputs found

    On triply even binary codes

    Full text link
    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

    Full text link
    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 k2\lceil\frac{k}{2}\rceil, and the cyclotomic number (0,0) is at most k21\lceil\frac{k}{2}\rceil-1, 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

    and

    No full text
    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
    corecore