90 research outputs found
Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound
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
Explicit MDS Codes with Complementary Duals
In 1964, Massey introduced a class of codes with complementary duals which
are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD
codes have applications in communication system, side-channel attack (SCA) and
so on. LCD codes have been extensively studied in literature. On the other
hand, MDS codes form an optimal family of classical codes which have wide
applications in both theory and practice. The main purpose of this paper is to
give an explicit construction of several classes of LCD MDS codes, using tools
from algebraic function fields. We exemplify this construction and obtain
several classes of explicit LCD MDS codes for the odd characteristic case
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