01204211/activity8 polynomials and graph theory 1
- This is part of 01204211-58.
In-class activities
Polynomials
- To work on these questions, you can refer to this lecture note from Berkeley.
For this set of activities, we shall work modulo 11.
We will use your student ID as a data. For , let denote the -th digit (counting from the lest, starting at 0) of your student ID. For example if your student ID is 5755543210, , , ,
A.1-1 We shall use your last 4 digits: . Find a polynomial of degree 3 such that for . You should start by writing down .
A.1-2 Let's experiment on erasure code using the degree 3 polynomial from the last question. Let's treat the first 4 digits of your ID as a message. We will encode it into 6 pairs of numbers (modulo 11) like this: , , , , , .
Note that the first 4 pairs represent your message exactly. The last 2 pairs provide extra information.