Quasi-cyclic self-dual codes with four factors
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In this study, we examine $\ell$-quasi-cyclic self-dual codes of length $\ell m$ over $\mathbb{F}_2$, provided that the polynomial $X^m-1$ has exactly four distinct irreducible factors in $\mathbb{F}_2[X]$. We find the standard form of generator matrices of codes over the ring $R \cong \mathbb{F}_q[X]/(X^m-1)$ and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths $2$ and $4$ over $R$.
Abstract
In this study, we examine $\ell$-quasi-cyclic self-dual codes of length $\ell m$ over $\mathbb{F}_2$, provided that the polynomial $X^m-1$ has exactly four distinct irreducible factors in $\mathbb{F}_2[X]$. We find the standard form of generator matrices of codes over the ring $R \cong \mathbb{F}_q[X]/(X^m-1)$ and the conditions for the codes to be self-dual. We explicitly determine the forms of generator matrices of self-dual codes of lengths $2$ and $4$ over $R$.
참고문헌 (15)
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