A Finite Gilbert–Varshamov Bound for Pure Stabilizer Quantum Codes

Abstract

A finite Gilbert-Varshamov (GV) bound for pure stabilizer (binary and nonbinary) quantum error correcting codes is presented in analogy to the GV bound for classical codes by using several enumerative results in finite unitary geometry. From this quantum GV bound we obtain several new binary quantum codes in a nonconstructive way having better parameters than the known codes.