Abstract
AbstractAugmented orthogonal arrays (AOAs) were introduced by Stinson, who showed the equivalence between ideal ramp schemes and AOAs (Discrete Math. 341 (2018), 299–307). In this paper, we show that there is an AOA if and only if there is an OA which can be partitioned into subarrays, each being an OA, and that there is a linear AOA if and only if there is a linear maximum distance separable (MDS) code of length and dimension over , which contains a linear MDS subcode of length and dimension over . Some constructions for AOAs and some new infinite classes of AOAs are also given.
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