Additive cyclic codes over Fq3

Shi, Minjia and Chu, Shixiao and Özbudak, Ferruh (2025) Additive cyclic codes over Fq3. Journal of Algebra and its Applications, 24 (09). ISSN 0219-4988 (Print) 1793-6829 (Online)

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Abstract

Let Fq be an arbitrary finite field and n ≥ 2 be an integer with gcd(n,q) = 1. We study all Fq-linear additive cyclic codeseses over Fq3 of length n systematically. This much more complicated compared to the same task over Fq2. We obtain a canonical unique representation. We explicitly obtain the dual codes in the canonical form under the Euclidean and trace the Galois inner products. We characterize and construct large classes of complementary dual codes among Fq-linear additive cyclic codes over Fq3 of length n under the trace Euclidean and the trace Galois inner products. We obtain interesting differences depending on the canonical representation and also on the inner products. We also study subfield subcodes and trace (onto Fq) codes.
Item Type: Article
Uncontrolled Keywords: Additive codes; cyclic codes; dual codes
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Ferruh Özbudak
Date Deposited: 08 Aug 2025 12:15
Last Modified: 08 Aug 2025 12:15
URI: https://research.sabanciuniv.edu/id/eprint/51840

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