Single parity-check code ($C=\{x\in {\mathbb{F}}_2^n:{\sum }_i{x}_i=0\}$)

The code consisting of all even-weight binary words. For $n\ge 1$ 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.