# Efficient Description of some Classes of Codes using Group Algebras

@article{ChimalDzul2022EfficientDO, title={Efficient Description of some Classes of Codes using Group Algebras}, author={Henry Chimal-Dzul and Niklas Gassner and Joachim Rosenthal and Reto Schnyder}, journal={ArXiv}, year={2022}, volume={abs/2208.04061} }

Circulant matrices are an important tool widely used in coding theory and cryptography. A circulant matrix is a square matrix whose rows are the cyclic shifts of the ﬁrst row. Such a matrix can be eﬃciently stored in memory because it is fully speciﬁed by its ﬁrst row. The ring of n × n circulant matrices can be identiﬁed with the quotient ring F [ x ] / ( x n − 1). In consequence, the strong algebraic structure of the ring F [ x ] / ( x n − 1) can be used to study properties of the collection…

## One Citation

### Left ideal LRPC codes and a ROLLO-type cryptosystem based on group algebras

- Mathematics, Computer ScienceArXiv
- 2022

Left ideal low-rank parity-check codes are introduced by using group algebras and they are used to extend KEM.

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