Computer Algebra Subject name : Cyclic Codes Writing F4 = F2[@]/(a? + a + 1), consider the ideal I = (x2 + ay2 + ay, x + 1) in F4[x,y]/(x3 1, y3 1). a) Write the corresponding ideal J. b) Show that the reduced Grbner basis of J with respect to lex order x > y is G = {y2 + ay + a,x + 1} c) Find all monomials w E LT(G) in which each variable x and y appears to a power at most 2. d) Find G for each w in part c. e) Encode these monomials using E(w) = w - WG. Computer Algebra Subject name : Cyclic Codes Writing F4 = F2[@]/(a? + a + 1), consider the ideal I = (x2 + ay2 + ay, x + 1) in F4[x,y]/(x3 1, y3 1). a) Write the corresponding ideal J. b) Show that the reduced Grbner basis of J with respect to lex order x > y is G = {y2 + ay + a,x + 1} c) Find all monomials w E LT(G) in which each variable x and y appears to a power at most 2. d) Find G for each w in part c. e) Encode these monomials using E(w) = w - WG