2009/12/30 by Stephan Foldes, Foldes, Stephan, László Major +2
Computer Science · Engineering · Mathematics · #05C12 #06F99 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05C12 #msc:06F99
paper · pdf · doi:10.48550/arxiv.1001.0046
6 pages
openalex publication_date 2009/12/30 · arxiv created 2009/12/31 · arxiv updated 2010/01/14 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
The Cayley graph construction provides a natural grid structure on a finite vector space over a field of prime or prime square cardinality, where the characteristic is congruent to 3 modulo 4, in addition to the quadratic residue tournament structure on the prime subfield. Distance from the null vector in the grid graph defines a Manhattan norm. The Hermitian inner product on these spaces over finite fields behaves in some respects similarly to the real and complex case. An analogue of the Cauchy-Schwarz inequality is valid with respect to the Manhattan norm. With respect to the non-transitive order provided by the quadratic residue tournament, an analogue of the Cauchy-Schwarz inequality holds in arbitrarily large neighborhoods of the null vector, when the characteristic is an appropriate large prime.