2014/04/30 by C. Salazar-Lazaro, Carlos Salazar-Lazaro, Salazar-Lazaro, Carlos
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1405.0045
arxiv created 2014/04/30 · openalex publication_date 2014/04/30 · arxiv updated 2014/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A skew Hadamard difference set (SHDS) is a difference set that satisfies the skew condition. It is known that if a group G admits a skew hadamard difference set, then G is a p-group with order congruent to 3 modulo 4. We will generalize skew Hadamard difference sets to Generalized Skew Hadamard Difference Sets (GSHDS) to cover the case when p is congruent to 1 module 4, and we will extend all known results that yield necessary existence conditions of skew Hadamard difference sets to our generalization, including the known exponent bounds. We will also show a set of necessary existence conditions a special family of groups. We will close the article with a general p-divisibility condition of the difference intersection numbers of a GSHDS for a special class of subgroups L.