Goncharov's relations in Bloch's higher Chow group CH3(F,5)

In this paper we will prove Goncharov's 22-term relations (see [A.B. Goncharov, Geometry of configurations, polylogarithms and motivic cohomology, Adv. Math. 114 (1995) 179–319. [G1]]) in the linearized version of Bloch's higher Chow group CH3(F,5) using linear fractional cycles of Bloch, Kriz and Totaro under the Beilinson–Soulé vanishing conjecture that CH2(F,n)=0 for n⩾4.