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

Lingfei Jin; Chaoping Xing

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arXiv · 1703.01441

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

Lingfei Jin·Chaoping Xing

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Abstract

It was shown by Massey that linear complementary dual (LCD for short) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound still remains to be the best asymptotical lower bound for LCD codes. In this paper, we show that an algebraic geometry code over a finite field of even characteristic is equivalent to an LCD code and consequently there exists a family of LCD codes that are equivalent to algebraic geometry codes and exceed the asymptotical GV bound.

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Lingfei Jin, Chaoping Xing. 2017-03-04. Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound. https://arxiv.org/abs/1703.01441

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