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arXiv · 2506.10381

Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings

Sanjit Bhowmick·Kuntal Deka·Alexandre Fotue Tabue·Edgar Martínez-Moro
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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.

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Sanjit Bhowmick, Kuntal Deka, Alexandre Fotue Tabue, Edgar Martínez-Moro. 2025-06-12. Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings. https://arxiv.org/abs/2506.10381

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