A decomposition of the 2-design formed by the planes in AG(2n, 3)

Abstract It is well known that for a prime power s and a positive integer m, the set of d-flats in AG ( m , s ) forms a 2-design. In this article, it is shown that the 2-design formed by the 2-flats in AG ( m , 3 ) for even m can be decomposed into more subdesigns than a previously known decomposition. Exact calculation of the number of the resulting subdesigns is also demonstrated by examining the distribution of points in cyclotomic cosets.

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