Groebner bases, Geometric codes and Order Domains

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 will be provided to all participants.

Total number of lectures: 30 hours.

Monday 9.00-13.00

Tuesday 9.00-13.00, 15.00-18.00

Wednesday 9.00-13.00

Workshop 14.30-18.30

Thursday 9.00-13.00, 14.00-17.00

Friday 9.00-13.00

Saturday 9.00-13.00

Some participants

• Monica La Barbiera (Messina)

• Luca Barletta (Milano-Poli)

• Daniele Bartoli (Perugia)

• Marcus Bishop (Galway-Ireland)

• Fabrizio Caruso (Trento)

• Stefania Fanali (Perugia)

• Davide Frapporti (Trento)

• Marco Frego (Trento)

• Olav Geil (Aalborg-Denmark)

• Luca Goldoni (Trento)

• Teo Mora (Genova)

• Padraig O'Cathai (Galway-Ireland)

• Marco Pizzato (Trento)

• Hamid Rahkooy (Linz-Austria)

• Anna Rimoldi (Trento)

• Massimiliano Sala (Trento)

• Christian Spagnol (Cork-Ireland)

• Paola Stagliano (Messina)

• Adnen Sboui (Ankara)

We provide complete food and accomodation (Agritur Ponte Alto), including the dinner of Sunday 7-th (when people are supposed to arrive) and the breakfast of Sunday 14-th (when people are supposed to leave).
150 euros only for non-Italians 350 euros for Italians.

These are the results of an anonymous questionnaire circulated through the (non-local) participants.

G=Good, F=Fair, B=Bad,

• How do you judge food and accommodation? ---> 100% G

• Were lectures interesting ? ---------------> 90% G, 10% F

• Were lecture notes informative? -----------> 100% G

• Did you find it useful? -------------------> 50% G, 50% F

• Was the related workshop interesting? -----> 80% G, 20% F

• Would you consider coming back? -----------> 100% G

• Would you suggest this to your colleagues? 90% G, 10% F

• Overall evaluation ------------------------> 100% G