Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings
Information Theory
2025-06-13 v1 math.IT
Abstract
This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are free modules. Moreover, we present a necessary and sufficient condition for a pair of additive cyclic codes over a finite commutative ring to form an additive complementary pair. Finally, we construct a complementary pair of additive cyclic codes over a finite chain ring and show that one of the codes is permutation equivalent to the trace dual of the other.
Keywords
Cite
@article{arxiv.2506.10381,
title = {Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings},
author = {Sanjit Bhowmick and Kuntal Deka and Alexandre Fotue Tabue and Edgar Martínez-Moro},
journal= {arXiv preprint arXiv:2506.10381},
year = {2025}
}