**Reading assignment:**

**Peterson & Weldon, "Error-Correcting Codes," MIT Press, (Second Edition), (1986), Chapter 7.****Gill, "Linear Sequential Circuits," McGraw-Hill, (1966), Chapter 2.**

**Problem 1.**

**(a) Draw the linear sequential circuit (LSC) that multiplies by the polynomial**

**
h(x)
= 1 + x ^{3} +x^{6}**

**(b) Draw the linear sequential circuit (LSC) that divides by the polynomial**

**
g(x) = 1 + x ^{2}
+ x^{4} + x^{6} + x^{7}**

**(c) Draw the linear sequential circuit (LSC) that simultaneously multiplies by h(x) and divides by g(x).**

**Problem 2.** **
Draw an LSC which takes as inputs polynomials
a(x) and
b(x) and then
produces the output h(x)a(x) + k(x)b(x),
where h(x)
and k(x)
are the polynomials:**

**
h(x) = 1 + x ^{4} + x^{10}
and k(x) = x + x^{2} + x^{4}
+ x^{7} + x^{9}**