engleski

Symmetric designs with primitive automorphism groups of degree less than 256

We have constructed and classified all primitive (v, k, &#955; )-symmetric designs with v<256. The starting points were the well-known Kantor's result (1985) on symmetric designs with 2-transitive automorphism groups, and the fact that Paley difference sets yield a series of primitive symmetric designs. Several algorithms for construction have been developed with two different approaches to the problem, depending on whether v is prime or not. It proves that, up to isomorphism, there exist exactly 71 primitive (v, k, &#955; )-symmetric designs, 2k<v<256. We characterize them in relation to primitive groups action, the full automorphism group included

Symmetric design; automorphism group; primitive action; difference set

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