Finding the Maximum Number of Symbols for the 4b/10b Line Code with Error Correction

In this paper, we present 20 symbols for the error correcting 4b/10b line coding scheme, increasing the number of available symbols from the 18 originally proposed. The two additional symbols are used to supplement special control codes and increase compatibility with other line codes such as 8b/10b. In addition, we show that the 20 found is the maximum number of symbols possible for 4b/10b by formulating the problem as the maximum clique problem, an NP-hard problem. Finally, we show that the generalized problem of finding a set with the maximum number of symbols is NP-hard as well.