Efficient Description of some Classes of Codes using Group Algebras

  title={Efficient Description of some Classes of Codes using Group Algebras},
  author={Henry Chimal-Dzul and Niklas Gassner and Joachim Rosenthal and Reto Schnyder},
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… 

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