= Parity congruence description of tetracode lattices
{title2=$x\bmod3\in T,\quad x_1\equiv\cdots\equiv x_4\pmod2$}
Add respectively the conditions $\sum_i x_i\equiv0\pmod4$ and $\sum_i x_i-2x_1\equiv0\pmod4$ to the displayed common conditions. These define the two integer <Euclidean lattices> underlying the <tetracode length-isospectral lattice construction>. They coincide on their all-even vectors and differ on all-odd vectors. Reflecting a coordinate divisible by three preserves the code condition; on odd vectors it changes the coordinate sum by two modulo four, while on even vectors both conditions remain satisfied. This yields the <coordinate reflection bijection for tetracode lattices>.
Back to article page
