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arXiv · 2603.07177

Construction of Multicyclic Codes of Arbitrary Dimension $r$ via Idempotents: A Unified Combinatorial-Algebraic Approach

Jean Charles Ramanandraibe·Ramamonjy Andriamifidisoa
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Abstract

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.

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Jean Charles Ramanandraibe, Ramamonjy Andriamifidisoa. 2026-03-07. Construction of Multicyclic Codes of Arbitrary Dimension $r$ via Idempotents: A Unified Combinatorial-Algebraic Approach. https://arxiv.org/abs/2603.07177

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