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)
This is the latest version of this item.
Official URL: https://dx.doi.org/10.1142/S0219498825503396
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 |
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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 |
Available Versions of this Item
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Additive cyclic codes over Fq3. (deposited 18 Sep 2024 16:03)
- Additive cyclic codes over Fq3. (deposited 08 Aug 2025 12:15) [Currently Displayed]