On The Dimension of The Subfield Subcodes of 1-Point Hermitian Codes

TL;DR

This paper determines the true dimension of subfield subcodes of 1-point Hermitian codes, including non-binary cases, which is crucial for their application in post-quantum cryptography.

Contribution

It provides new explicit values for the dimension of subfield subcodes of 1-point Hermitian codes, advancing understanding of their parameters for cryptographic use.

Findings

New dimension values for subfield subcodes of 1-point Hermitian codes

Includes non-binary subfield cases

Enhances cryptographic code parameter knowledge

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 $1$--point Hermitian codes, including the case when the subfield is not binary.