Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound

摘要

It was shown by Massey that linear complementary dual (LCD for short) codesare asymptotically good. In 2004, Sendrier proved that LCD codes meet theasymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV boundstill remains to be the best asymptotical lower bound for LCD codes. In thispaper, we show that an algebraic geometry code over a finite field of evencharacteristic is equivalent to an LCD code and consequently there exists afamily of LCD codes that are equivalent to algebraic geometry codes and exceedthe asymptotical GV bound.