In this article, we consider decoding Grassmann codes, linear codes associated to the Grassmannian and its embedding in a projective space. We look at the orbit structure of Grassmannian arising from the multiplicative group${\mathbb {F}}_{q^{m}}^{*}$in$GL_{m}(q)$. We project the corresponding Grassmann code onto these orbits to obtain a subcode of a$q$–ary Reed-Solomon code. We prove that some of these projections contain an information set of the parent Grassmann code. By improving the decoding capacity of Peterson’s decoding algorithm for the projected subcodes, we prove that one can correct up to$\lfloor (d-1)/2\rfloor $errors for Grassmann code, where$d$is the minimum distance of Grassmann code.

In this article, we consider Schubert codes, linear codes associated to Schubert varieties, and discuss minimum weight codewords for dual Schubert codes. The notion of lines in Schubert varieties is looked closely at, and it has been proved that the supports of the minimum weight codewords of the dual Schubert codes lie on lines and any three points on a line in the Schubert variety correspond to the support of some minimum weight parity check for the Schubert code. We use these lines in Schubert varieties to construct orthogonal parity checks for certain Schubert codes and use them for majority logic decoding. In some special cases, we can correct approximately up to$\lfloor (d-1)/2\rfloor $many errors where$d$is the minimum distance of the code.