Reproduce “A Characterization of $q$-Ary $2$-Designs and a $3$-Design Obstruction for Doubly-Extended Reed-Solomon Codes” on OpenResearch
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About this paper
Guanghui Zhang, Zhengbang Zha
The authors classify q-ary designs in doubly extended Reed–Solomon codes. These designs require fixed-weight codewords to cover every prescribed nonzero-symbol assignment on selected coordinates equally often, not merely to balance supports. Every nonempty positive-weight class is a 2-design exactly when gcd(k−1, q−1)=1. No class of weight 3 to q is a 3-design; full-support strength 3 remains unresolved.
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