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 𝔽n 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.
@article{bwmeta1.element.doi-10_1515_math-2017-0093,
author = {Mar\'\i a Isabel Garc\'\i a-Planas and Dolors Maria Magret and Laurence Emilie Um},
title = {Monomial codes seen as invariant subspaces},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1099-1107},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0093}
}
María Isabel García-Planas; Dolors Maria Magret; Laurence Emilie Um. Monomial codes seen as invariant subspaces. Open Mathematics, Tome 15 (2017) pp. 1099-1107. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0093/