-->>Please note change in email address till December
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| David Glynn | Internet: Glynn@math.uni-kiel.de |
| Mathematisches Seminar | Home Phone: +49 431 57532 |
| University of Kiel | Work Phone: +49 431 880 3663 |
| Kiel, D-24105, Germany | Time Zone : GMT +1 hour |
+------Ao (cloud) tea (white) roa (long) = Aotearoa (New Zealand)-----+
Title: New Results about Geometric Codes
David Glynn, Uni. of Canterbury, Christchurch, Neuseeland, or
Te Whare Wananga o Waitaha, Otautahi, Te Wai Pounamu, Aotearoa;
zur Zeit an der Uni. zu Kiel.
Abstract: Consider the collection of all i-dimensional subspaces
of PG(n,q), the finite projective space of dimension n over the
finite field GF(q). The geometric code C_i(n,q) is then the
vector space of all functions from the points of PG(n,q) to
GF(q), such that the sum over all points of any subspace of
dimension i is zero. This code is dual to D_i(n,q), which is
generated by the characteristic functions of the subspaces of
dimension m. We shall explain how these codes are formed using
algebraic functions: there are natural bases using monomials.
As an example, we can determine precisely when two of the codes are
orthogonal. Basically, C_i is orthogonal to C_j (or equivalently
C_i is contained in D_j) when q=p^h, and h is small enough,
(where p is the characteristic of GF(q)).
This is joint work with Baskhar Bagchi of the Indian Statistical
Institute in Bangalore.