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.