2020•Advances in Mathematics of CommunicationsOpen access

On the dimension of the subfield subcodes of 1-point Hermitian codes

Sabira El Khalfaoui, Gábor P. Nagy

Abstract

Subfield subcodes of algebraic-geometric codes are good candidates for the use in post-quantum cryptosystems, provided their true parameters such as dimension and minimum distance can be determined. In this paper we present new values of the true dimension of subfield subcodes of \begin{document}$ 1 $\end{document} –point Hermitian codes, including the case when the subfield is not binary.

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Key concepts: Mathematics, Dimension (graph theory), Hermitian matrix, Point (geometry), Algebraic number, Discrete mathematics, Pure mathematics, Binary number