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Constructions of augmented orthogonal arrays
Author(s) -
Wang Xin,
Ji Lijun,
Li Yun,
Liang Miao
Publication year - 2018
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21624
Subject(s) - mathematics , dimension (graph theory) , equivalence (formal languages) , separable space , combinatorics , ideal (ethics) , code (set theory) , discrete mathematics , computer science , mathematical analysis , philosophy , set (abstract data type) , epistemology , programming language
Augmented 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 ( s , t , k , v ) if and only if there is an OA ( t , k , v ) which can be partitioned into v t − ssubarrays, each being an OA ( s , k , v ) , and that there is a linear AOA ( s , t , k , q ) if and only if there is a linear maximum distance separable (MDS) code of length k and dimension t over F q , which contains a linear MDS subcode of length k and dimension s over F q . Some constructions for AOAs and some new infinite classes of AOAs are also given.