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首页> 外文期刊>Journal of Discrete Mathematical Sciences and Cryptography >Modified linear block code with code rate 1/2 and less than 1/2
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Modified linear block code with code rate 1/2 and less than 1/2

机译：修改了线性块代码，代码率1/2且小于1/2

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This work proposes a new code which can be considered as the modification of linear block code with code rate 1/2 and less than 1/2. The theme of the work is derived from the controllability of discrete time system and accordingly the generator matrix is chosen. A procedure is proposed in this paper which can transform the lower dimensional space to higher dimensional space. A Code is subspace of a space, so, with the help of addition of an equivalent identity matrix, between I (Identity matrix) and P (Parity Check) matrix of the established generator matrix, the lower dimensional space is transformed to higher dimensional space. Multiple numbers of errors could be corrected with the help of this designed code. It is also shown that decoding of this code can be established using the methods like syndrome detection and nearest neighbor decoding. The proposed code satisfies all the bounds. The minimum distance d, which could be achieved here, is at least equal to the total no. of information bits which enhances its error correction capacity.
机译：这项工作提出了一种新的代码，可以被视为用代码率1/2和小于1/2的线性块代码的修改。该工作的主题是从离散时间系统的可控性导出的，因此选择了发电机矩阵。本文提出了一种过程，其可以将较低的尺寸空间转变为更高的尺寸空间。代码是空间的子空间，因此，在添加等效标识矩阵的帮助下，在我（标识矩阵）和建立的发生器矩阵的P（奇偶校验）矩阵之间，较低的尺寸空间被转换为更高的尺寸空间。在这个设计的代码的帮助下可以纠正多个错误。还显示，可以使用校正综合检测和最近的邻解码的方法建立该代码的解码。所提出的代码满足所有界限。这里可以实现的最小距离D至少等于总体。信息位提高其纠错容量。

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