Generalized LRPC codes
Information Theory
2023-05-04 v1 math.IT
Abstract
In this paper we generalize the notion of low-rank parity check (LRPC) codes by introducing a bilinear product over F^m q based on a generic 3-tensor in Fq^mxmxm, where Fq is the finite field with q elements. The generalized LRPC codes are Fq -linear codes in general and a particular choice of the 3-tensor corresponds to the original Fqm -linear LRPC codes. For the generalized LRPC codes, we propose two probabilistic polynomial-time decoding algorithms by adapting the decoding method for LRPC codes and also show that the proposed algorithms have a decoding failure rate similar to that of decoding LRPC codes
Cite
@article{arxiv.2305.02053,
title = {Generalized LRPC codes},
author = {Ermes Franch and Philippe Gaborit and Chunlei Li},
journal= {arXiv preprint arXiv:2305.02053},
year = {2023}
}
Comments
A shorter version of this paper was presented in ITW 2023