2026-04-15T01:04:43Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/796982025-11-14T20:00:53Zcom_10324_1145com_10324_931com_10324_894col_10324_1254

Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings Bhowmick, Sanjit Deka, Kuntal Fotue Tabue, Alexandre Martínez Moro, Edgar Additive cyclic codes Additive complementary pairs Trace dual Finite chain ring 1201 Álgebra Producción Científica This paper investigates the algebraic structure of complemen- tary pairs of additive cyclic codes over a finite commutative chain ring of odd characteristic. We demonstrate that for every additive complementary pair of additive codes, both constituent codes are free modules. Moreover, we present a necessary and sufficient condition for a pair of additive codes over a finite commutative chain ring of odd characteristic to form an additive complementary pair. Finally, we show that, in the case of a complementary pair of additive cyclic codes over a finite chain ring of odd characteristic, one of the codes is permutation equivalent to the trace dual of the other. 2025-11-14T13:59:13Z 2025-11-14T13:59:13Z 2026 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Finite Fields and Their Applications, 2026, vol. 110, p. 102732 1071-5797 https://uvadoc.uva.es/handle/10324/79698 10.1016/j.ffa.2025.102732 102732 Finite Fields and Their Applications 110 eng https://www.sciencedirect.com/science/article/pii/S1071579725001625 Attribution-NonCommercial-NoDerivatives 4.0 Internacional info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2025 The Author(s) application/pdf Elsevier https://uvadoc.uva.es/bitstream/10324/79698/4/Trace-duality-and-additive-complementary.pdf.jpg Hispana TEXT http://creativecommons.org/licenses/by-nc-nd/4.0/ UVaDOC. Repositorio Documental de la Universidad de Valladolid https://uvadoc.uva.es/handle/10324/79698