We propose a technique of selecting seeds for the LFSR-based test pattern generators that are used in VLSI BISTs. By setting the computed seed as an initial value, target fault coverage, for example 100%, can be accomplished with minimum test length. We can also maximize fault coverage for a given test length. Our method can be used for both test-per-clock and test-per-scan BISTs. The procedure is based on vector representations over GF(2m), where m is the number of LFSR stages. The results indicate that test lengths derived through selected seeds are about sixty percent shorter than those derived by simple seeds, i.e. 0001, for a given fault coverage. We also show that seeds obtained through this technique accomplish higher fault coverage than the conventional selection procedure. In terms of the c7552 benchmark, taking a test-per-scan architecture with a 20-bit LFSR as an example, the number of undetected faults can be decreased from 304 to 227 for 10,000 LFSR patterns using our proposed technique.