On generator matrices and parity check matrices of generalized integer codes
On generator matrices and parity check matrices of generalized integer codes
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DOI：
10.1007/s10623-013-9883-7
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
H. Matsui
中科院分区：
文献类型：
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作者：
H. Matsui
广义整数码定义为模整数环上的码，其中各个码元通常具有不同的模。本文利用一类矩阵恒等式，导出了整数矩阵等于广义整数码的生成矩阵的一个充要条件。此外，它示出的奇偶校验矩阵生成从这个矩阵单位的生成矩阵。我们还证明了一类整数码的列表与Hecke环之间的密切联系。最后，给出了一个有效的算法，从理论上枚举出广义整数码的所有生成矩阵。
Generalized integer codes are defined as codes over rings of integers moduloin which individual code symbols generally have different moduli. In this paper, we use a certain type of matrix identities to derive a necessary and sufficient condition for integer matrices to be equal to the generator matrices of generalized integer codes. Moreover, it is shown that the parity check matrix is generated from this matrix identity of the generator matrix. We also show the close connection between the listing of a certain type of integer codes and Hecke rings. Finally, an efficient algorithm that enumerates theoretically all of the generator matrices of generalized integer codes is provided.