• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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## Section: New Results

### Fast transforms over fields of characteristic 2

Participant : Nicholas Coxon.

With the aim of reaching fast, linear time, algorithms for encoding multiplicity codes, which have good local properties, N. Coxon had to develop subalgorithms for dealing with the Hermite interpolation [13], which in turn relies on computer algebra for fast transforms over fields of characteritic two [14]. Locally decodable codes are used for private information retrieval, where a database can be privately queried by a user, in such a way that the user does not reveal his query. Using codes with locality for private information retrieval, the database is first encoded, then queried using the local property of the code. Since the databases in question can be large, only linear time algorithms can be used. Our results achieve linear-time complexity, and even with a non agressively optimized implementation, can encode as much as ${10}^{9}$ bits in thirty seconds on a laptop.