On ag-fold jointm-spotty Lee weight enumerator

<p style='text-indent:20px;'>This paper mainly study <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes. A Gray map from <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{Z}_{2}^{\alpha}\times\mathbb{Z}_{4}^{\beta}[u] $\end{document}</tex-math></inline-formula> to <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{Z}_{4}^{\alpha+2\beta} $\end{document}</tex-math></inline-formula> is defined, and we prove that is a weight preserving and distance preserving map. A MacWilliams-type identity between the Lee weight enumerator of a <inline-formula><tex-math id="M5">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive code and its dual is proved. Some properties of one-weight <inline-formula><tex-math id="M6">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes and two-weight projective <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes are discussed. As main results, some construction methods for one-weight and two-weight <inline-formula><tex-math id="M8">\begin{document}$ \mathbb{Z}_{2}\mathbb{Z}_{4}[u] $\end{document}</tex-math></inline-formula>-additive codes are studied, meanwhile several examples are presented to illustrate the methods.</p>

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MacWilliams Type Identity for M-Spotty Rosenbloom-Tsfasman Weight Enumerator of Linear Codes over Finite Ring

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e96.a.1496 ◽

2013 ◽

Vol E96.A (6) ◽

pp. 1496-1500

Author(s):

Jianzhang CHEN ◽

Wenguang LONG ◽

Bo FU

Keyword(s):

Linear Codes ◽

Finite Ring ◽

Weight Enumerator ◽

Type Identity

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Construction of two-Lee weight codes over

International Journal of Computer Mathematics ◽

10.1080/00207160.2014.989709 ◽

2014 ◽

Vol 93 (3) ◽

pp. 415-424 ◽

Cited By ~ 5

Author(s):

Minjia Shi ◽

Lou Chen

Keyword(s):

Lee Weight

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A restriction on the weight enumerator of a self-dual code

Journal of Combinatorial Theory Series A ◽

10.1016/0097-3165(76)90071-6 ◽

1976 ◽

Vol 21 (2) ◽

pp. 253-255 ◽

Cited By ~ 14

Author(s):

Harold N Ward

Keyword(s):

Dual Code ◽

Weight Enumerator

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Nonexistence of Certain Singly Even Self-Dual Codes with Minimal Shadow

The Electronic Journal of Combinatorics ◽

10.37236/7155 ◽

2018 ◽

Vol 25 (1) ◽

Cited By ~ 1

Author(s):

Stefka Bouyuklieva ◽

Masaaki Harada ◽

Akihiro Munemasa

Keyword(s):

Minimum Weight ◽

Dual Code ◽

Weight Enumerator ◽

Dual Codes

It is known that there is no extremal singly even self-dual $[n,n/2,d]$ code with minimal shadow for $(n,d)=(24m+2,4m+4)$, $(24m+4,4m+4)$, $(24m+6,4m+4)$, $(24m+10,4m+4)$ and $(24m+22,4m+6)$. In this paper, we study singly even self-dual codes with minimal shadow having minimum weight $d-2$ for these $(n,d)$. For $n=24m+2$, $24m+4$ and $24m+10$, we show that the weight enumerator of a singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow is uniquely determined and we also show that there is no singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow for $m \ge 155$, $m \ge 156$ and $m \ge 160$, respectively. We demonstrate that the weight enumerator of a singly even self-dual code with minimal shadow is not uniquely determined for parameters $[24m+6,12m+3,4m+2]$ and $[24m+22,12m+11,4m+4]$.

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