id: 06513091
dt: j
an: 2016a.00852
au: Brown, Ezra
ti: Many more names of $(7, 3, 1)$.
so: Math. Mag. 88, No. 2, 103-120 (2015).
py: 2015
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: K20 P20 F60 H40
ut: block designs; binary Hamming code; $q$-ary Hamming code; Singer designs;
Singer difference sets; sums of squares; octonions; sedenions
ci: Zbl 1064.05031
li: doi:10.4169/math.mag.88.2.103
ab: 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,
83‒94 (2002; Zbl 1064.05031)] described $(7, 3, 1)$’s connection
with such areas as graph theory, number theory, topology, round-robin
tournaments, and algebraic number fields. In this paper, we show how
$(7, 3, 1)$ makes appearances in the areas of error-correcting codes,
$n$-dimensional finite projective geometries, difference sets, normed
algebras, and the three-circle Venn diagram.
rv: