Fractional decoding of r-Hermitian codes

In this paper, we present a fractional decoding algorithm for a new family of codes which are constructed from the Hermitian curve, called r-Hermitian codes. These codes of length n are defined over an extension field Fq2l of Fq2 and the fractional decoding algorithms that we present are algorithms for error correction that use only αln symbols of a subfield of size q2 as input into the decoding algorithm, where α<1, meaning a fraction of the subsymbols that are typically utilized. We demonstrate that collaborative decoding of interleaved codes supports fractional decoding of the r-Hermitian codes, allowing for improved bounds on the fractional decoding radius.