论文标题
2乘2个块矩阵结构和组环的新的自偶长68的自偶代码68
New Self-Dual Codes of length 68 from a 2 by 2 block matrix Construction and Group Rings
论文作者
论文摘要
许多用于构建不同长度的极端二进制自动二元代码的发电机矩阵具有g =（i | a）的形式，其中i是n by n by n个身份矩阵，而a是由第一行完全确定的n矩阵。在这项工作中，我们定义了一个发电机矩阵，其中a是一个块矩阵，其中块来自组环，而且a也不由出现在第一行中的元素完全确定。 By applying our construction over F_2+uF_2 and by employing the extension method for codes, we were able to construct new extremal binary self-dual codes of length 68. Additionally, by employing a generalised neighbour method to the codes obtained, we were able to construct many new binary self-dual [68,34,12]-codes with the rare parameters gamma=7,8 and 9 in W_{68,2}.特别是，我们发现了92个新的二进制自动偶数[68,34,12] - 编码。
Many generator matrices for constructing extremal binary self-dual codes of different lengths have the form G=(I|A), where I is the n by n identity matrix and A is the n by n matrix fully determined by the first row. In this work, we define a generator matrix in which A is a block matrix, where the blocks come from group rings and also, A is not fully determined by the elements appearing in the first row. By applying our construction over F_2+uF_2 and by employing the extension method for codes, we were able to construct new extremal binary self-dual codes of length 68. Additionally, by employing a generalised neighbour method to the codes obtained, we were able to construct many new binary self-dual [68,34,12]-codes with the rare parameters gamma=7,8 and 9 in W_{68,2}. In particular, we find 92 new binary self-dual [68,34,12]-codes.
