
06513091
j
2016a.00852
Brown, Ezra
Many more names of $(7, 3, 1)$.
Math. Mag. 88, No. 2, 103120 (2015).
2015
Mathematical Association of America (MAA), Washington, DC
EN
K20
P20
F60
H40
block designs
binary Hamming code
$q$ary Hamming code
Singer designs
Singer difference sets
sums of squares
octonions
sedenions
Zbl 1064.05031
doi:10.4169/math.mag.88.2.103
Summary: The $(7, 3, 1)$ block design is an object that shows up in many areas of mathematics. In fact, $(7, 3, 1)$ seems to appear again and again in unexpected places. [{\it E. Brown}, Math. Mag. 75, No. 2, 8394 (2002; Zbl 1064.05031)] described $(7, 3, 1)$'s connection with such areas as graph theory, number theory, topology, roundrobin tournaments, and algebraic number fields. In this paper, we show how $(7, 3, 1)$ makes appearances in the areas of errorcorrecting codes, $n$dimensional finite projective geometries, difference sets, normed algebras, and the threecircle Venn diagram.