$t$-Frobenius Negacyclic Codes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866916228394647552 |
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| author | Bag, Priyabrata Dey, Santanu |
| author_facet | Bag, Priyabrata Dey, Santanu |
| contents | Let $\mathbb{F}_p$ denote the finite field of order $p$, where $p$ is an odd prime. We study certain quantum negacyclic codes over $\mathbb{F}_p$ which we call $t$-Frobenius negacyclic codes. We obtain a criterion for constructing such codes from certain subspaces of $\mathbb{F}_p^n\times\mathbb{F}_p^n$ in terms of generating pairs of ideals of cyclotomic rings and we completely classify all linear $t$-Frobenius negacyclic codes. Further, the notion of BCH distance is extended for these codes and several new codes are identified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_02580 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | $t$-Frobenius Negacyclic Codes Bag, Priyabrata Dey, Santanu Quantum Physics 81P70, 94B15 Let $\mathbb{F}_p$ denote the finite field of order $p$, where $p$ is an odd prime. We study certain quantum negacyclic codes over $\mathbb{F}_p$ which we call $t$-Frobenius negacyclic codes. We obtain a criterion for constructing such codes from certain subspaces of $\mathbb{F}_p^n\times\mathbb{F}_p^n$ in terms of generating pairs of ideals of cyclotomic rings and we completely classify all linear $t$-Frobenius negacyclic codes. Further, the notion of BCH distance is extended for these codes and several new codes are identified. |
| title | $t$-Frobenius Negacyclic Codes |
| topic | Quantum Physics 81P70, 94B15 |
| url | https://arxiv.org/abs/1709.02580 |