Generalized low rank parity check codes

Abstract

In this work we propose a family of Fq-linear lowrank parity check (LRPC) codes based on a bilinear product over Fmq defined by a generic 3-tensor over Fq. A particular choice of this tensor corresponds to the classical Fqm-linear LRPC codes; and other tensors yield Fq-linear codes, which, with some caveats, can be efficiently decoded with the same idea of decoding LRPC codes. The proposed codes contribute to the diversity of rank metric codes for cryptographic applications, particularly for the cases where attacks utilize Fqm-linearity to reduce decoding complexity.