计算机工程与应用
計算機工程與應用
계산궤공정여응용
COMPUTER ENGINEERING AND APPLICATIONS
2014年
18期
113-117
,共5页
幂等生成元%剩余码%循环码
冪等生成元%剩餘碼%循環碼
멱등생성원%잉여마%순배마
generating idempotent%residue code%cyclic code
有限域上高次剩余码的生成多项式都是多项式xn-1的因式。针对多项式xn-1在有限域上分解的困难性，给出了三元域F3上三次和四次剩余码的幂等生成元表达式。利用计算机软件求解这些幂等生成元与xn-1最大公因式就可得到三次和四次剩余码生成多项式而不用分解xn-1。
有限域上高次剩餘碼的生成多項式都是多項式xn-1的因式。針對多項式xn-1在有限域上分解的睏難性，給齣瞭三元域F3上三次和四次剩餘碼的冪等生成元錶達式。利用計算機軟件求解這些冪等生成元與xn-1最大公因式就可得到三次和四次剩餘碼生成多項式而不用分解xn-1。
유한역상고차잉여마적생성다항식도시다항식xn-1적인식。침대다항식xn-1재유한역상분해적곤난성，급출료삼원역F3상삼차화사차잉여마적멱등생성원표체식。이용계산궤연건구해저사멱등생성원여xn-1최대공인식취가득도삼차화사차잉여마생성다항식이불용분해xn-1。
The generating polynomials of higher degree residue codes over finite fields are factors of the polynomial xn-1 . Generally speaking, it is difficult to factor the polynomial xn-1 over finite fields. This paper gives generating idempotents of cubic and quartic residue codes over the field F3 . As a result, the generating polynomials of cubic and quartic residue codes over the field F3 can be obtained by computing the greatest common divisors of these generating idempotents and the polynomial xn-1 with computer software such as Matlab and Maple.
