  The energy used to transmit a single bit of data between the devices in
wireless networks is equal to the energy for performing hundreds of
instructions in those devices. Thus the reduction of the data necessary to
transmit, while keeping the same functionality of the employed algorithms is a
formidable and challenging scientific task. We describe an algorithm called
Small Set of Allowed Coefficients (SSAC) that produces the shortest header
overhead in random linear network coding schemes compared with all other
approaches reported in the literature. The header overhead length is 2 to 7
times shorter than the length achieved by related compression techniques. For
example, SSAC algorithm compresses the length of the header overhead in a
generation of 128 packets to 24 bits, while the closest best result achieved by
an algorithm based on error correcting codes has a header overhead length of 84
bits in $GF(16)$ and 224 bits in $GF(256)$. We show that the header length in
SSAC does not depend on the size of the finite field where the operations are
performed, i.e., it just depends on the number of combined packets $m$.
