Correction from lecture 04
Written on 29.11.2022 17:16 by Stella Wohnig
I got a bit overly excited in saying the Covering bound is an upper bound. It is of course a lower bound :D Lecture recording will be up soon.
To make the distinction clear:
A lower bound describes what is Definitely achievable in terms of code dimension/number of codewords. So a code with the given number of codewords definitely exists, better codes MAY.
An upper bound describes a boundary above which codes cannot exist, this does not guarantee a code of that cardinality, it just says that no code with more words can possibly exist.