Update: I had another look at this. Actually, in retrospect, the substance of the lecture notes are not wrong, but they are worded for electronic engineers rather than computer scientists or mathematicians
Normally one would present the process of creating a code word in the form:
Where is the code word, is the message to be coded and the generator matrix. The lecture notes present the generator matrix in a systematic form which would be the equivalent of:
, where is the identity matrix.
Here’s a quandry: you are researching “Cyclic Redundancy Codes” (CRCs) – mainly for finding a clearer way to explain them, when you come across some lecture notes from an academic at one of the bigger universities in Western Europe which, initially at least, look like a model of clear exposition. But as you read on, you realise with growing incredulity that what the lecturer describes as CRCs are not CRCs at all but general linear block codes. Now, the principles are similar – in that the lecturer discusses generator matrices and parity check matrices, but the details are hopelessly wrong. So, do you (a) denounce the academic in public, or (b) contact them in private or (c) post a ‘blind’ blog and wonder about what value students and taxpayers are getting for their money?