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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/2506.03688 |
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Table of Contents:
- An orthogonal array (OA), denoted by $\text{OA}(M, n, q, t)$, is an $M \times n$ matrix over an alphabet of size $q$ such that every selection of $t$ columns contains each possible $t$-tuple exactly $λ=M / q^t$ times. An irredundant orthogonal array (IrOA) is an OA with the additional property that, in any selection of $n - t$ columns, all resulting rows are distinct. IrOAs were first introduced by Goyeneche and Życzkowski in 2014 to construct $t$-uniform quantum states without redundant information. Beyond their quantum applications, we focus on IrOAs as a combinatorial and coding theory problem. An OA is an IrOA if and only if its minimum Hamming distance is at least $t + 1$. Using this characterization, we demonstrate that for any linear code, either the code itself or its Euclidean dual forms a linear IrOA, giving a huge source of IrOAs. In the special case of self-dual codes, both the code and its dual yield IrOAs. Moreover, we construct new families of linear IrOAs based on self-dual, Maximum Distance Separable (MDS), and MDS-self-dual codes. Finally, we establish bounds on the minimum distance and covering radius of IrOAs.