TABLE OF CONTENTS Minimal polynomials have important applications in the implementation of many binary sequences with good correlation, such as 3-term sequences, 5-term sequences, most of the signal sets with low cross-correlation, and the boolean functions transformed from trace representations of sequences. For these applications, we need to compute the minimal polynomials of elements in finite fields. In this appendix, we list the minimal polynomials of elements in 
for 5 ? n ? 10. For example, for ? i ? , the corresponding minimal polynomial of ? i is equal to the polynomial
where s is the smallest number such that i2 s ? i (mod 2 n 1). We represent this as a vector ( c 0 , c 1 , ,c s 1 , c s) where s n. For example, for n = 6 in Table 3.8, the minimal polynomial of ? 3 is given as 
, and the minimal polynomial of ? 9 is given as 
.
| n = 5 | n = 6 | ||
|---|---|---|---|
| Coset leader i | | Coset leader i | |
| 1 | 100101 | 1 | 1100001 |
| 3 | 111101 | 3 | 1110101 |
| 5 | 110111 | 5 | 1110011 |
| 7 | 101111 | 7 | 1001001 |
| 11 | 111011 | 9 | 1011 |
| 15 | 101001 | 11 | 1011011 |
