Monomial codes seen as invariant subspaces - García-Planas, María Isabel; Magret, Maria Dolors; Um, Laurence Emilie (Open mathematics (Warsaw, Poland), 2017)
It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field 𝔽 and hyperinvariant subspaces of 𝔽 under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.