Single parity-check code
= Single parity-check code
{title2=$C=\{x\in\mathbb F_2^n:\sum_i x_i=0\}$}
= Simple parity check code
{synonym}
The code consisting of all even-weight binary words. For $n\geq1$ its dimension is $n-1$, and its <weight enumerator> is $[(t+s)^n+(t-s)^n]/2$, by selecting the even terms of the <binomial theorem>. The length-one code contains only zero.