11,260 research outputs found
Some new quasi-twisted ternary linear codes
Let code be a linear code of length , dimension and minimum Hamming distance over . One of the basic and most important problems in coding theory is to construct codes with best possible minimum distances. In this paper seven quasi-twisted ternary linear codes are constructed. These codes are new and improve the best known lower bounds on the minimum distance in [6]
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
Binary and Ternary Quasi-perfect Codes with Small Dimensions
The aim of this work is a systematic investigation of the possible parameters
of quasi-perfect (QP) binary and ternary linear codes of small dimensions and
preparing a complete classification of all such codes. First we give a list of
infinite families of QP codes which includes all binary, ternary and quaternary
codes known to is. We continue further with a list of sporadic examples of
binary and ternary QP codes. Later we present the results of our investigation
where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions
up to 13 are classified.Comment: 4 page
On Optimal Family of Codes for Archival DNA Storage
DNA based storage systems received attention by many researchers. This
includes archival and re-writable random access DNA based storage systems. In
this work, we have developed an efficient technique to encode the data into DNA
sequence by using non-linear families of ternary codes. In particular, we
proposes an algorithm to encode data into DNA with high information storage
density and better error correction using a sub code of Golay code.
Theoretically, 115 exabytes (EB) data can be stored in one gram of DNA by our
method.Comment: Supplementary file and the software DNA Cloud 2.0 is available at
http://www.guptalab.org/dnacloud This is the preliminary version of the paper
that appeared in Proceedings of IWSDA 2015, pp. 143--14
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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