Abstract
We prove that there exist non-Abelian group codes over an arbitrary finite field.
Similar content being viewed by others
References
S. D. Berman, “On the theory of group codes,” Cybernetics, 3, 31–99 (1967).
J. J. Bernal, Á. del Río, and J. J. Simón, “An intrinsical description of group codes,” Designs, Codes Cryptogr., 51, No. 3, 289–300 (2009).
E. Couselo, S. González, V. Markov, and A. Nechaev, “Loop codes,” Discrete Math. Appl., 14, No. 2, 163–172 (2004).
C. García Pillado, S. González, V. Markov, C. Martínez, and A. Nechaev, “Group codes which are not Abelian group codes,” in: Proc. of the Third Int. Castle Meeting on Coding Theory and Applications, pp. 123–127 (2011).
C. García Pillado, S. González, V. T. Markov, C. Martínez, and A. A. Nechaev, “Non-Abelian group codes,” Uch. Zap. Orlovsk. Gos. Univ., 6, No. 2, 73–79 (2012).
C. García Pillado, S. González, V. T. Markov, C. Martínez, and A. A. Nechaev, “When all group codes of a noncommutative group are Abelian (a computational approach)?” J. Math. Sci., 186, No. 4, 578–585 (2012).
C. García Pillado, S. González, V. T. Markov, C. Martínez, and A. A. Nechaev, “Group codes over non-Abelian groups,” J. Algebra Appl., 12, No. 7, 135037 (2013).
V. T. Markov, “Abelian and non-Abelian group codes over noncommutative groups,” in: Algebra and Number Theory: Contemporary Problems and Applications, Proc. of the XIIth Int. Conf. dedicated to 80th birthday of Prof. Victor Nikolaevich Latyshev. Tula, April 21–25, 2014 [in Russian], L. N. Tolstoy TGPU, Tula (2014), pp. 200–203.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 20, No. 1, pp. 17–22, 2015.
Rights and permissions
About this article
Cite this article
García Pillado, C., González, S., Markov, V.T. et al. Non-Abelian Group Codes over an Arbitrary Finite Field. J Math Sci 223, 504–507 (2017). https://doi.org/10.1007/s10958-017-3363-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3363-y