 
Summary: 269 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 46, NO. 1, JANUARY 2000
Then
f0(x)f2(x) =(x 08)(x + 8)(x 01) = x3
+ 01x2
+ x 01
f0(x)f1(x) =(x 08)(x + 1) = x2
07x 08:
Let C be the code such that C = hff0(x)f2(x); 13f0(x)f1(x)gi. We
note that the code is also nonfree. Then rank(C) = 40deg(f0(x)) =
3 and d(C) = 2 = 4 03 + 1. So the code is also MDR.
A. Chinese Remainder Theorem of RS Codes
We shall show how the CRT construction applies to RS codes. Let
n be a divisor of gcd(1(pm
1 ); 111; 1(pm
s )), with k = s
i=1 pm
i ,
where i is an element of p satisfying the conditions given above.
Namely, i is a unit, n=1
i , j
