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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.11765 |
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| _version_ | 1866915199734251520 |
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| author | Chibloun, Abdelghaffar Ou-azzou, Hassan Martínez-Moro, Edgar Najmeddine, Mustapha |
| author_facet | Chibloun, Abdelghaffar Ou-azzou, Hassan Martínez-Moro, Edgar Najmeddine, Mustapha |
| contents | In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree $n$ over a finite chain ring $ R.$ We extend the concepts of $ n $-isometry and $ n $-equivalence known for constacyclic codes to this class of codes, providing a broader framework for their structural analysis. We describe the classes of $n$-equivalence and compute their number, significantly reducing the study of trinomial codes over $R$. Additionally, we examine the special case of trinomials of the form $ x^n - a_1x - a_0 \in R[x] $ and analyze their implications. Finally, we consider the extension of our results to certain trinomial additive codes over $ R.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On polycyclic linear and additive codes associated to a trinomial over a finite chain ring Chibloun, Abdelghaffar Ou-azzou, Hassan Martínez-Moro, Edgar Najmeddine, Mustapha Information Theory In this paper, we investigate polycyclic codes associated with a trinomial of arbitrary degree $n$ over a finite chain ring $ R.$ We extend the concepts of $ n $-isometry and $ n $-equivalence known for constacyclic codes to this class of codes, providing a broader framework for their structural analysis. We describe the classes of $n$-equivalence and compute their number, significantly reducing the study of trinomial codes over $R$. Additionally, we examine the special case of trinomials of the form $ x^n - a_1x - a_0 \in R[x] $ and analyze their implications. Finally, we consider the extension of our results to certain trinomial additive codes over $ R.$ |
| title | On polycyclic linear and additive codes associated to a trinomial over a finite chain ring |
| topic | Information Theory |
| url | https://arxiv.org/abs/2503.11765 |