Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-correction capability of a code and its minimum distance can be established. Generalizing their Hamming-metric counterparts, upper and lower bounds on the cardinality of a code with a given weighted-Hamming distance are obtained. Finally, we propose a simple code construction with optimal minimum distance for specific parameters.

翻译：独立并行的q元对称信道适用于多种应用场景的传输模型。本文提出的加权汉明度量针对该场景量身定制，能够实现最优解码性能。研究表明，某些加权汉明度量码具备独特性质——所有超过最小距离一半的错误均可被纠正。尽管如此，仍可建立纠错能力与最小距离之间的紧密关联。通过推广汉明度量下的对应结果，我们获得了给定加权汉明距离下码字基数上下界的表达式。最后，针对特定参数提出了一种具有最优最小距离的简单码构造方法。