On q-ary linear completely regular codes with ρ=2 and antipodal dual
On q-ary linear completely regular codes with ρ=2 and antipodal dual
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DOI：
10.3934/amc.2010.4.567
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发表时间：
2010-11
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影响因子：
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通讯作者：
J. Borges;J. Rifà;V. Zinoviev
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文献类型：
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作者：
J. Borges;J. Rifà;V. Zinoviev
我们刻画了所有覆盖半径$\rho=2$的q元线性完全正则码的对偶码是对跖码时的特征.这些完全正则码是覆盖半径为1的线性完全正则码的推广，我们也对其进行了分类。对于$\rho=2$，我们给出了已知的所有此类码的列表。这也给出了两个重量线性对跖码的特征。最后，对一类覆盖半径为2且具有对映对偶的完全正则码，指出了自对偶和提升码的一些有趣性质.
We characterize all $q$-ary linear completely regular codes with covering radius $\rho=2$ when the dual codes are antipodal. These completely regular codes are extensions of linear completely regular codes with covering radius 1, which we also classify. For $\rho=2$, we give a list of all such codes known to us. This also gives the characterization of two weight linear antipodal codes. Finally, for a class of completely regular codes with covering radius $\rho=2$ and antipodal dual, some interesting properties on self-duality and lifted codes are pointed out.