The error-correction code based proof-of-work (ECCPoW) algorithm is based on a low-density parity-check (LDPC) code. The ECCPoW is possible to impair ASIC with its time-varying capability of the parameters of LDPC code. Previous researches on the ECCPoW algorithm have presented its theory and implementation on Bitcoin. But they do not discuss how stable the block generation time is. A finite mean block generation time (BGT) and none heavy-tail BGT distribution are the ones of the focus in this study. In the ECCPoW algorithm, BGT may show a long-tailed distribution due to time-varying cryptographic puzzles. Thus, it is of interest to see if the BGT distribution is not heavy-tailed and if it shows a finite mean. If the distribution is heavy-tailed, then confirmation of a transaction cannot be guaranteed. We present implementation, simulation, and validation of ECCPoW Ethereum. In implementation, we explain how the ECCPoW algorithm is integrated into Ethereum 1.0 as a new consensus algorithm. In the simulation, we perform a multinode simulation to show that the ECCPoW Ethereum works well with automatic difficulty change. In the validation, we present the statistical results of the two-sample Anderson-Darling test to show that the distribution of BGT satisfies the necessary condition of the exponential distribution. Our implementation is downloadable at https://github.com/cryptoecc/ETH-ECC.