PROJECT TITLE :

Sub-Quadratic Decoding of One-Point Hermitian Codes

ABSTRACT:

We tend to gift the primary 2 sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first relies on a quick realization of the Guruswami–Sudan algorithm using state-of-the-art algorithms from laptop algebra for polynomial-ring matrix minimization. The second is a power decoding algorithm: an extension of classical key equation decoding that offers a probabilistic decoding algorithm up to the Sudan radius. We tend to show how the ensuing key equations can be solved by the matrix minimization algorithms from laptop algebra, yielding similar asymptotic complexities.