49 research outputs found
On MDS Negacyclic LCD Codes
Linear codes with complementary duals (LCD) have a great deal of significance
amongst linear codes. Maximum distance separable (MDS) codes are also an
important class of linear codes since they achieve the greatest error
correcting and detecting capabilities for fixed length and dimension. The
construction of linear codes that are both LCD and MDS is a hard task in coding
theory. In this paper, we study the constructions of LCD codes that are MDS
from negacyclic codes over finite fields of odd prime power elements. We
construct four families of MDS negacyclic LCD codes of length
, and a family of negacyclic LCD codes
of length . Furthermore, we obtain five families of -ary
Hermitian MDS negacyclic LCD codes of length and four
families of Hermitian negacyclic LCD codes of length For both
Euclidean and Hermitian cases the dimensions of these codes are determined and
for some classes the minimum distances are settled. For the other cases, by
studying and -cyclotomic classes we give lower bounds on the minimum
distance
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