$\mathbb{F}_q\mathbb{F}_{q^2}$-additive cyclic codes and their Gray images

Ankit Yadav; Ritumoni Sarma

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arXiv · 2511.02325

$\mathbb{F}_q\mathbb{F}_{q^2}$-additive cyclic codes and their Gray images

Ankit Yadav·Ritumoni Sarma

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Abstract

We investigate additive cyclic codes over the alphabet $\mathbb{F}_{q}\mathbb{F}_{q^2}$, where $q$ is a prime power. First, its generator polynomials and minimal spanning set are determined. Then, examples of $\mathbb{F}_{q^2}$-additive cyclic codes that satisfy the well-known Singleton bound are constructed. Using a Gray map, we produce certain optimal linear codes over $\mathbb{F}_{3}$. Finally, we obtain a few optimal ternary linear complementary dual (LCD) codes from $\mathbb{F}_{3}\mathbb{F}_{9}$-additive codes.

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Ankit Yadav, Ritumoni Sarma. 2025-11-04. $\mathbb{F}_q\mathbb{F}_{q^2}$-additive cyclic codes and their Gray images. https://arxiv.org/abs/2511.02325

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