Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.07177 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917321517301760 |
|---|---|
| author | Ramanandraibe, Jean Charles Andriamifidisoa, Ramamonjy |
| author_facet | Ramanandraibe, Jean Charles Andriamifidisoa, Ramamonjy |
| contents | We propose a unified method to construct multicyclic codes of arbitrary dimension $r$ over $\mathbb{F}_q$. The approach relies on $r$-dimensional primitive idempotents defined as tensor products of univariate ones, combined with multidimensional cyclotomic orbits. This establishes a direct equivalence between combinatorial and algebraic descriptions, yields a natural polynomial basis, and provides an optimal product bound generalizing BCH and Reed-Solomon bounds. An efficient constructive algorithm is presented and illustrated by optimal 3-dimensional codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07177 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of Multicyclic Codes of Arbitrary Dimension $r$ via Idempotents: A Unified Combinatorial-Algebraic Approach Ramanandraibe, Jean Charles Andriamifidisoa, Ramamonjy Commutative Algebra 2020 : 94B15 (Primary), 94B05, 11T71 (Secondary) We propose a unified method to construct multicyclic codes of arbitrary dimension $r$ over $\mathbb{F}_q$. The approach relies on $r$-dimensional primitive idempotents defined as tensor products of univariate ones, combined with multidimensional cyclotomic orbits. This establishes a direct equivalence between combinatorial and algebraic descriptions, yields a natural polynomial basis, and provides an optimal product bound generalizing BCH and Reed-Solomon bounds. An efficient constructive algorithm is presented and illustrated by optimal 3-dimensional codes. |
| title | Construction of Multicyclic Codes of Arbitrary Dimension $r$ via Idempotents: A Unified Combinatorial-Algebraic Approach |
| topic | Commutative Algebra 2020 : 94B15 (Primary), 94B05, 11T71 (Secondary) |
| url | https://arxiv.org/abs/2603.07177 |