Shortened Hamming Codes Maximizing Double Error Detection

Abstract

Given $r\ge 3$ and $2^{r-1}+1\le n<2^r-1$, an $[n,n-r,3]$ shortened Hamming code that can detect a maximal number of double errors is constructed. The optimality of the construction is proven.

We withdraw the paper since we found a reference from 1981 that solves exactly the same problem