1. A vector coding method, comprising: decomposing an initial vector to obtain a sign vector and an initial absolute vector, wherein each respective vector has a plurality of elements; coding the sign vector to obtain a sign code; performing multi-level permutation-based coding on the initial absolute vector to obtain an absolute vector code; and combining the sign code and the absolute vector code to obtain a code of the initial vector; wherein performing multi-level permutation-based coding on the initial absolute vector to obtain an absolute vector code includes: removing from the plurality of elements of the initial absolute vector any element having an element value which satisfies a preset condition; constructing a new absolute vector with each of the plurality of elements not satisfying the preset condition; coding positions of each of the plurality of elements not satisfying the preset condition in the initial absolute vector to obtain a position code; proceeding with the multi-level permutation-based coding on the new absolute vector if the number of element values in the new absolute vector is larger than 1; and obtaining the absolute vector code by combining all the position codes obtained in the multi-level permutation-based coding if the number of element values in the new absolute vector is 1.