On the classification of self-dual [20,10,9] codes over GF(7)

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• 作者：Masaaki Harada ; ^{mharada@m.tohoku.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Akihiro Munemasa ^{munemasa@math.is.tohoku.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：94B05
• 刊名：Finite Fields and Their Applications
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：42
• 期：Complete
• 页码：57-66
• 全文大小：274 K

文摘

It is shown that the extended quadratic residue code of length 20 over 07157971630034X&_mathId=si1.gif&_user=111111111&_pii=S107157971630034X&_rdoc=1&_issn=10715797&md5=7ccd81d8de796d576d80c810291e5399" title="Click to view the MathML source">GF(7)$\mathrm{GF}(7)$ is a unique self-dual 07157971630034X&_mathId=si16.gif&_user=111111111&_pii=S107157971630034X&_rdoc=1&_issn=10715797&md5=63cb9119871b41ec21fa9595386493c1" title="Click to view the MathML source">[20,10,9]$[20,10,9]$ code C such that the lattice obtained from C   by Construction A is isomorphic to the 20-dimensional unimodular lattice 07157971630034X&_mathId=si13.gif&_user=111111111&_pii=S107157971630034X&_rdoc=1&_issn=10715797&md5=7e0778ea77038cc850698c4f427c88dc">07157971630034X-si13.gif">$D_{20}^{+}$, up to equivalence. This is done by converting the classification of such self-dual codes to that of skew-Hadamard matrices of order 20.