Geodesic
Nonexistence of certain singly even self-dual codes with minimal shadow
Stefka Bouyuklieva1 ; Masaaki Harada2 ; Akihiro Munemasa2
1Veliko Tarnovo University
2Tohoku University
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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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 $[24m+22,12m+11,4m+4]$.
DOI : 10.37236/7155
Classification : 94B05
Mots-clés : self-dual code, shadow, weight enumerator

Stefka Bouyuklieva  1   ; Masaaki Harada  2   ; Akihiro Munemasa  2

1 Veliko Tarnovo University
2 Tohoku University 
@article{10_37236_7155,
     author = {Stefka Bouyuklieva and Masaaki Harada and Akihiro Munemasa},
     title = {Nonexistence of certain singly even self-dual codes with minimal shadow},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {1},
     doi = {10.37236/7155},
     zbl = {1387.94111},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7155/}
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Stefka Bouyuklieva; Masaaki Harada; Akihiro Munemasa. Nonexistence of certain singly even self-dual codes with minimal shadow. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7155

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