2020/02/19 by Prasant Singh, Singh, Prasant · 1 citation
Computer Science · Engineering · Medicine · #14G50 #14M15 #94B05 #94B35 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Peptidase Inhibition and Analysis #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2002.08054
openalex publication_date 2020/02/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this article, we consider Schubert codes, linear codes associated to\nSchubert varieties, and discuss minimum weight codewords for dual Schubert\ncodes. The notion of lines in Schubert varieties is looked closely at, and it\nhas been proved that the supports of the minimum weight codewords of the dual\nSchubert codes lie on lines and any three points on a line in Schubert variety\ncorrespond to the support of some minimum weight parity check for the Schubert\ncode. We use these lines in Schubert varieties to construct orthogonal parity\nchecks for certain Schubert codes and use them for majority logic decoding. In\nsome special cases, we can correct approximately up to lfloor (d-1)/2 rfloor\nmany errors where d is the minimum distance of the code.\n