We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental parameters of binary error-correcting codes, both of which measure the probability that the maximum likelihood decoder fails. We then derive various bounds for the cardinality and weight distribution of a binary code in terms of these new parameters, giving examples of codes meeting the bounds with equality.

翻译：我们引入了二进制矢量之间的差异概念,二进制矢量不是一般的衡量函数,而是同时捕捉二进制不对称信道的数学结构。 反过来,这又导致二进制错误校正代码的两个新的基本参数,这两个参数都测量了最大可能解码器失灵的可能性。 然后,我们从这些新参数中得出了二进制代码的基度和重量分布的不同界限,并举例说明了以平等方式满足界限的代码。