4,350 research outputs found
Four infinite families of ternary cyclic codes with a square-root-like lower bound
Cyclic codes are an interesting type of linear codes and have wide
applications in communication and storage systems due to their efficient
encoding and decoding algorithms. Inspired by the recent work on binary cyclic
codes published in IEEE Trans. Inf. Theory, vol. 68, no. 12, pp. 7842-7849,
2022, and the arXiv paper arXiv:2301.06446, the objectives of this paper are
the construction and analyses of four infinite families of ternary cyclic codes
with length for odd and dimension
whose minimum distances have a square-root-like lower bound. Their duals have
parameters , where and
also has a square-root-like lower bound. These families of codes and
their duals contain distance-optimal cyclic codes
On extremal self-dual ternary codes of length 48
All extremal ternary codes of length 48 that have some automorphism of prime
order are equivalent to one of the two known codes, the Pless code or
the extended quadratic residue code
Five Families of Three-Weight Ternary Cyclic Codes and Their Duals
As a subclass of linear codes, cyclic codes have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, five families of
three-weight ternary cyclic codes whose duals have two zeros are presented. The
weight distributions of the five families of cyclic codes are settled. The
duals of two families of the cyclic codes are optimal
New binary and ternary LCD codes
LCD codes are linear codes with important cryptographic applications.
Recently, a method has been presented to transform any linear code into an LCD
code with the same parameters when it is supported on a finite field with
cardinality larger than 3. Hence, the study of LCD codes is mainly open for
binary and ternary fields. Subfield-subcodes of -affine variety codes are a
generalization of BCH codes which have been successfully used for constructing
good quantum codes. We describe binary and ternary LCD codes constructed as
subfield-subcodes of -affine variety codes and provide some new and good LCD
codes coming from this construction
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