2019/08/21 by Ricardo A. Podestá, Podestá, Ricardo A., Denis E. Videla +1
Computer Science · Engineering · Mathematics · #94B15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1908.08097
openalex publication_date 2019/08/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
For q=pm with p prime and k\| q-1, we consider the generalized Paley\ngraph \Γ(k,q) = Cay( mathbbFq, Rk), with Rk= xk : x \∈\n mathbbFq^* , and the irreducible p-ary cyclic code \C(k,q) =\n ( textrmTrq/p(\γ \ωik)i=0n-1) _\γ \∈\n mathbbFq, with \ω a primitive element of mathbbFq and\nn= tfracq-1k. We first express the spectra of \Γ(k,q) in terms of\nGaussian periods. Then, we show that the spectra of \Γ(k,q) and\n\C(k,q) are mutually determined by each other if further k\|\n tfracq-1p-1. We give Spec(\Γ(k,q)) explicitly for those graphs\nassociated with irreducible 2-weight cyclic codes in the semiprimitive and\nexceptional cases. We also compute Spec(\Γ(3,q)) and Spec(\Γ(4,q)).\n