有限域上的重根自对偶负循环码

Repeated-Root Self-Dual Negacyclic Codes over Finite Fields

中文关键词:  常循环码  负循环码  自对偶码  生成多项式

英文关键词:constacyclic codes  negacyclic codes  self-dual codes  generator polynomials

中文摘要:

      设$F_{q}$是一个有限域, $q=p^{m}$, $p$为素数.本文研究了$F_{q}$上的重根自对偶负循环码.研究了重根自对偶负循环码的计数问题.我们给出了$F_{q}$上的所有长度为$2^{a}p^{r}~(a\geq1)$的自对偶负循环码.我们还构造了$F_{q}$上长度为$2^{a}bp^{r}~(a\geq1)$的自对偶负循环码,这里${\rm gcd}(2,b)={\rm gcd}(b,p)=1$.

英文摘要:

      Let $F_{q}$ be a finite field with $q=p^{m}$, where $p$ is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over $F_{q}$. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length $2^{a}p^{r}$ over $F_{q}$, $a\geq1$. The construction of self-dual negacyclic codes of length $2^{a}bp^{r}$ over $F_{q}$ is also provided, where ${\rm gcd}(2,b)={\rm gcd}(b,p)=1$ and $a\geq1$.