An anticode of diameter at most 
is a set of words
whose pairwise Hamming distances are at most
. Unlike an error-correcting
code, which separates distinct codewords, an anticode
bounds their separation from above (Horlemann and Ravi 2026).
Let 
be the maximum size of an anticode
of length 
over the finite field 
, and let 
be the family of all such
anticodes. For fixed prime power 
and 
,
Horlemann and Ravi (2026) proved
 |
as 
, except when 
and 
.
The diameter 
may depend on 
.
At the excluded binary endpoint the exact count is 
, including the empty anticode.
A linear anticode is a subspace of 
with the stated diameter bound. Its support consists of
the coordinates that are nonzero in some member. Horlemann and Ravi (2026) credit
AI with suggesting support size as the organizing parameter for their related enumeration
of linear anticodes.
