On subspace designs
Copyright policy )On subspace designs
Guruswami and Xing introduced subspace designs in 2013 to give the first construction of positive rate rank metric codes list-decodable beyond half the distance. In this paper we provide bounds involving the parameters of a subspace design, showing they are tight via explicit constructions. We point out a connection with sum-rank metric codes, dealing with optimal codes and minimal codes with respect to this metric. Applications to two-intersection sets with respect to hyperplanes, two-weight codes, cutting blocking sets and lossless dimension expanders are also provided.
FOS: Computer and information sciences, sum-rank metric code, Computer Science - Information Theory, MSRD code, dimension expander, subspace evasive subspace, Linear codes and caps in Galois spaces, FOS: Mathematics, Mathematics - Combinatorics, s-design, subspace design, Spreads and packing problems in finite geometry, cutting design, Linear codes (general theory), Subject Classification (primary); (secondary). Subspace design; subspace evasive subspace; s-design; MSRD code; scattered subspace; sum-rank metric code; cutting design; dimension expander, Subject Classification (primary), Information Theory (cs.IT), \(s\)-design, Other designs, configurations, Combinatorics (math.CO), scattered subspace, Primary 51E23, 94B05. Secondary 51E22, 05B99, (secondary). Subspace design
FOS: Computer and information sciences, sum-rank metric code, Computer Science - Information Theory, MSRD code, dimension expander, subspace evasive subspace, Linear codes and caps in Galois spaces, FOS: Mathematics, Mathematics - Combinatorics, s-design, subspace design, Spreads and packing problems in finite geometry, cutting design, Linear codes (general theory), Subject Classification (primary); (secondary). Subspace design; subspace evasive subspace; s-design; MSRD code; scattered subspace; sum-rank metric code; cutting design; dimension expander, Subject Classification (primary), Information Theory (cs.IT), \(s\)-design, Other designs, configurations, Combinatorics (math.CO), scattered subspace, Primary 51E23, 94B05. Secondary 51E22, 05B99, (secondary). Subspace design
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