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Система компьютерной алгебры GAP: Groebner bases, Geometric codes and Order Domains



Summer School for Ph.D. students:
"Groebner bases, Geometric codes and Order Domains"

Dates: 8-13 June 2009 (Monday-Saturday).
Location: Dept. of Mathematics, Univ. of Trento, Italy.
Organizer: M. Sala (Trento, Italy).
Lecturers: O. Geil (Aalborg, Denmark), M. Sala (Trento, Italy).

Related event: Mini-Workshop in "Commutative Algebra and Codes,
10/6/2009,
(including talks by T. Mora and the lecturers).

Total number of lectures:30 hours.

Expected audience: 30 Ph.D. students/ young post-docs from Europe.

Course description:
Algebraic Geometry codes enjoy a rich mathematical structure and have
excellent properties, but they are difficult to explicitly encode/
decode.
Also, accurate estimates for their distance are difficult.
Recently, Order Domain codes have been proposed to partially bypass
these limitations by exploiting a pure Groebner basis approach with
explicit code constructions.

We will explain their properties, show how to compute their parameters
and how to decode them, with emphasis on Groebner basis theoretical
tools.
We will describe their relation to other codes, such as
one-point geometric Goppa codes and affine-variety codes.
We will provide all the necessary commutative algebra background,
including Groebner basis theory.
Some tutorials with programmes running on new computational facilities
will be given to help the students experiment with the methods exposed
in
the course.
Lecture notes covering the whole course will be given to all
participants.


Funding:
For 20 selected Ph.D. participants the following grant is provided.
They will pay a fee of 250 euros,
for which they will get food and accommodation
(from 7 June evening to 14 June morning).
The selection will be based on the students cv's.

For other participants, there will be no fee, they will have 5 lunches
for
free and they will be helped to find cheap food and accommodation.

Further info:
mail me -> sala@science.unitn.it
web page -> http://www.science.unitn.it/~sala/school.html

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