2012/10/21 by Tuvi Etzion, Etzion, Tuvi, Alexander Vardy +1 · 2 citations
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1210.5724
openalex publication_date 2012/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG(n,p) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are examined on two classical coding problems in the Grassmannian. The first is the existence of a parallelism with lines in the related projective geometry and the second is the existence of a Steiner structure. A computer search was applied to find parallelisms and codes. A new parallelism of lines in PG(5,3) was formed. A parallelism with these parameters was not known before. A large code which is only slightly short of a Steiner structure was formed.