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Sub-Quadratic Decoding of Gabidulin Codes

Research paper by Sven Puchinger, Antonia Wachter-Zeh

Indexed on: 13 Apr '16Published on: 13 Apr '16Published in: Computer Science - Information Theory



Abstract

This paper shows how to decode errors and erasures with Gabidulin codes in sub-quadratic time in the code length, improving previous algorithms which had at least quadratic complexity. The complexity reduction is achieved by accelerating operations on linearized polynomials. In particular, we present fast algorithms for division, multi-point evaluation and interpolation of linearized polynomials and show how to efficiently compute minimal subspace polynomials.