01204211/activity8 polynomials and graph theory 1

จาก Theory Wiki
ไปยังการนำทาง ไปยังการค้นหา
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.

Graph theory 1

Homework