Cyclic codes over the ring \(\mathbb{Z}_{2^k} + u\mathbb{Z}_{2^k}\) (Q6566478)
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scientific article; zbMATH DE number 7875521
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cyclic codes over the ring \(\mathbb{Z}_{2^k} + u\mathbb{Z}_{2^k}\) |
scientific article; zbMATH DE number 7875521 |
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Cyclic codes over the ring \(\mathbb{Z}_{2^k} + u\mathbb{Z}_{2^k}\) (English)
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3 July 2024
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The authors study finite non-chain Frobenius rings \(\mathcal{R}_k = \mathbb{Z}_{2^k} + u\mathbb{Z}_{2^k},\ k>1,\ u^2=0,\) and determine their sets of ideals. In particular the number of principal ideals is given. Then cyclic codes of odd length over \(\mathcal{R}_k\) are considered, and it is shown that these codes can be described by means of idempotent elements.
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finite ring
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Frobenius ring
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cyclic codes
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idempotent elements
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