Geodesic
The length of the group algebra of the dihedral group of order $2^k$
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 169-181

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In this paper, the length of the group algebra of a dihedral group in the modular case is computed under the assumption that the order of the group is a power of two. Various methods for studying the length of a group algebra in the modular case are considered. It is proved that the length of the group algebra of a dihedral group of order $2^{k+1} $ over an arbitrary field of characteristic $2$ is equal to $2^{k}$. 
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     author = {O. V. Markova and M. A. Khrystik},
     title = {The length of the group algebra of the dihedral group of order $2^k$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--181},
     publisher = {mathdoc},
     volume = {496},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a12/}
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O. V. Markova; M. A. Khrystik. The length of the group algebra of the dihedral group of order $2^k$. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 169-181. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a12/