Constacyclic codes of length $np^s$ over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t\rangle}$: Torsions and Cardinalities
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| Format: | Preprint |
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2026
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| _version_ | 1866917484765904896 |
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| author | Tiwari, Akanksha Kanwar, Pramod Sarma, Ritumoni |
| author_facet | Tiwari, Akanksha Kanwar, Pramod Sarma, Ritumoni |
| contents | The purpose of this article is to study constacyclic codes of length $np^s$ over $R^t:=\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle },$ where $t$ is a natural number and $\gcd(n,p)=1$. We give generators of all the ideals of $R^{t,n}_δ:=\frac{R^t[x]}{\langle x^{np^s}-δ\rangle},$ where $δ= δ_0+uδ_1+\dots+u^{t-1}δ_{t-1}$ is a unit in $R^t$. For $n=1,\ 2, \ 3$ and $t=3$, we provide all types of ideals (constacyclic codes) and also give the torsional degrees as well as cardinalities of these codes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11912 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constacyclic codes of length $np^s$ over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t\rangle}$: Torsions and Cardinalities Tiwari, Akanksha Kanwar, Pramod Sarma, Ritumoni Information Theory 94B05, 94B15, 16P70, 13C12 The purpose of this article is to study constacyclic codes of length $np^s$ over $R^t:=\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle },$ where $t$ is a natural number and $\gcd(n,p)=1$. We give generators of all the ideals of $R^{t,n}_δ:=\frac{R^t[x]}{\langle x^{np^s}-δ\rangle},$ where $δ= δ_0+uδ_1+\dots+u^{t-1}δ_{t-1}$ is a unit in $R^t$. For $n=1,\ 2, \ 3$ and $t=3$, we provide all types of ideals (constacyclic codes) and also give the torsional degrees as well as cardinalities of these codes. |
| title | Constacyclic codes of length $np^s$ over $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t\rangle}$: Torsions and Cardinalities |
| topic | Information Theory 94B05, 94B15, 16P70, 13C12 |
| url | https://arxiv.org/abs/2605.11912 |