论文标题
Hadamard矩阵与某个系列三元自偶代码有关
Hadamard matrices related to a certain series of ternary self-dual codes
论文作者
论文摘要
2013年，Nebe和Villar提供了一系列的三元自偶代码，长度为2美元（P+1）$，$ P $一致，$ 5 $ MODULO $ 8 $。结果，发现了第三个三元极端自动双重代码，长度为$ 60 $。我们表明，当$ p $一致至$ 5 $ modulo $ 24 $时，三元自偶代码包含订单$ 2（p+1）$的订单$ 2（p+1）$的代码字$ 24 $。此外，还表明三元自偶代码是由Hadamard矩阵的行生成的。我们还证明，第三个三元极端自动划分长度为$ 60 $，至少包含两个不等的hadamard矩阵。
In 2013, Nebe and Villar gave a series of ternary self-dual codes of length $2(p+1)$ for a prime $p$ congruent to $5$ modulo $8$. As a consequence, the third ternary extremal self-dual code of length $60$ was found. We show that the ternary self-dual code contains codewords which form a Hadamard matrix of order $2(p+1)$ when $p$ is congruent to $5$ modulo $24$. In addition, it is shown that the ternary self-dual code is generated by the rows of the Hadamard matrix. We also demonstrate that the third ternary extremal self-dual code of length $60$ contains at least two inequivalent Hadamard matrices.
