Paper 2025/114

Better Codes for the HQC Cryptosystem

Abstract

In the HQC cryptosystem, the length $n$ of the code determines several concrete parameters such as the bandwidth usage, the memory consumption, or the decoding efficiency. In this paper, we show that currently known methods to explicitly generate asymptotically good (especially with high relative distances), binary codes with efficient associated procedures cannot be used to improve $n$. We also show that concatenated codes are currently better suited, and by exhausting small codes, find a closer to optimal concatenated code for HQC, which improves upon currently used codes.