A new idea regarding the generation of a block code for a code rate of 1/2 and less than 1/2 is developed here. The minimum distance between the codewords can be maximised using a suitable transformation of the P matrix in the generator matrix G of the block code. This study gives the construction of distance increasing mapping (DIM) such that the proposed code is a variable distance modified block code with a code rate equal to 1/2. An algorithm for such DIM is developed here. The construction for distance preserving mapping (DPM) is also generalised in an algorithmic way. Further, to achieve DIM from the proposed DPM, for the established codes with a code rate less than 1/2, transformation is developed with the help of permutation arrays. The performance of the codes has also been evaluated. Decoding of this code is also simple and can be carried out using the existing techniques of decoding of block codes. The probability of undetected error is found to be better than the existing block codes.

中文翻译：

---

可变距离分组码的距离增加映射

在此，提出了关于以1/2的码率和小于1/2的码率生成分组码的新思想。码字之间的最小距离可以使用适当的变换来最大化。P 生成器矩阵中的矩阵 G块代码。这项研究给出了距离增加映射（DIM）的构造，以使所提出的代码是可变距离的修改后的块码，其码率等于1/2。这里开发了用于这种DIM的算法。距离保留映射（DPM）的构造也以算法方式进行了概括。此外，为了从建议的DPM中实现DIM，对于编码率小于1/2的已建立代码，借助置换阵列来开发变换。代码的性能也已得到评估。该代码的解码也很简单，并且可以使用现有的分组代码解码技术来执行。发现未检测到的错误的概率比现有的分组码更好。