2020/08/27 by Fernando Julio Piñero, Piñero, Fernando, Prasant Singh +1
Computer Science · #14G50 #14M15 #94B27 #94B35 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2008.12067
openalex publication_date 2020/08/27 · openalex created_date 2022/10/11 · openalex updated_date 2026/07/28
In this manuscript, we consider decoding Grassmann codes, linear codes associated to Grassmannian of planes in an affine space. We look at the orbit structure of Grassmannian arising from the natural action of multiplicative group of certain finite field extension. We project the corresponding Grassmann code onto these orbits to obtain a few subcodes of certain Reed-Solomon code. We prove that some of these projected codes contains an information set of the parent Grassmann code. By improving the efficiency 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.