Geodesic
A generalisation of quadratic residue codes to the case of cubic and biquadratic residues
Diskretnaya Matematika, Tome 17 (2005) no. 4, pp. 143-149
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In this paper, we consider a generalisation of quadratic residue codes to the cases of higher power residues. Such a generalisation enhances the information transmission rate with the use of such codes as compared with the quadratic-residue codes, at a sacrifice in the lower bound for the code distance, though. We consider the construction of generating polynomials for such codes, which allows to write explicitly their generating matrix. 
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     author = {D. N. Semenovykh},
     title = {A~generalisation of quadratic residue codes to the case of cubic and biquadratic residues},
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D. N. Semenovykh. A generalisation of quadratic residue codes to the case of cubic and biquadratic residues. Diskretnaya Matematika, Tome 17 (2005) no. 4, pp. 143-149. http://geodesic.mathdoc.fr/item/DM_2005_17_4_a12/

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[2] Ireland K., Rosen M., A classical introduction to modern number theory, Springer, New York, 1982 | MR | Zbl