Codes from flag varieties over a finite field
Algebraic-geometric error-correcting codes are usually constructed from algebraic curves over finite fields, as they were originally introduced by \textit{V. Goppa} [Math. USSR, Izv. 21, 75--91 (1983); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 46, 762--781 (1982; Zbl 0522.94013)]. \textit{S. Vladut} and \textit{Yu. Manin} [J. Soviet. Math. 30, 2611--2643 (1985); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 25, 209--257 (1984; Zbl 0629.94013)] showed how to construct codes from higher-dimensional varieties. In this article the author presents a family of codes arising from flag varieties over finite fields. To that end he follows the usual way of embedding a flag variety \(X\) into a projective space and then evaluating linear forms on \(X\) (as described in the book by \textit{M. Tsfasman} and \textit{S. Vladut} [Algebraic-geometric codes, Math. Appl., Sov. Ser. 58 (Dordrecht, Kluwer) (1991; Zbl 0727.94007)]). He also gives the parameters of the obtained codes in some cases.
scientific article; zbMATH DE number 1878477