2,073 research outputs found
Twisted Reed-Solomon Codes
We present a new general construction of MDS codes over a finite field
. We describe two explicit subclasses which contain new MDS codes
of length at least for all values of . Moreover, we show that
most of the new codes are not equivalent to a Reed-Solomon code.Comment: 5 pages, accepted at IEEE International Symposium on Information
Theory 201
New Non-Equivalent (Self-Dual) MDS Codes From Elliptic Curves
It is well known that MDS codes can be constructed as algebraic geometric
(AG) codes from elliptic curves. It is always interesting to construct new
non-equivalent MDS codes and self-dual MDS codes. In recent years several
constructions of new self-dual MDS codes from the generalized twisted
Reed-Solomon codes were proposed. In this paper we construct new non-equivalent
MDS and almost MDS codes from elliptic curve codes. 1) We show that there are
many MDS AG codes from elliptic curves defined over for any given
small consecutive lengths , which are not equivalent to Reed-Solomon codes
and twisted Reed-Solomon codes. 2) New self-dual MDS AG codes over from elliptic curves are constructed, which are not equivalent to
Reed-Solomon codes and twisted Reed-Solomon codes. 3) Twisted versions of some
elliptic curve codes are introduced such that new non-equivalent almost MDS
codes are constructed. Moreover there are some non-equivalent MDS elliptic
curve codes with the same length and the same dimension. The application to MDS
entanglement-assisted quantum codes is given.We also construct non-equivalent
new MDS codes of short lengths from higher genus curves.Comment: 28 pages, new non-equivalent MDS codes from higher genus curves are
discusse
Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography
We present a generalisation of Twisted Reed-Solomon codes containing a new
large class of MDS codes. We prove that the code class contains a large
subfamily that is closed under duality. Furthermore, we study the Schur squares
of the new codes and show that their dimension is often large. Using these
structural properties, we single out a subfamily of the new codes which could
be considered for code-based cryptography: These codes resist some existing
structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the
code parameters from an obfuscated generator matrix.Comment: 5 pages, accepted at: IEEE International Symposium on Information
Theory 201
Hulls of special typed linear codes and constructions of new EAQECCs
In this paper, we study Euclidean and Hermitian hulls of generalized
Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the
Hermitian hulls of Roth-Lempel typed codes. We present explicit constructions
of MDS and AMDS linear codes for which their hull dimensions are well
determined. As an application, we provide several classes of
entanglement-assisted quantum error correcting codes with new parameters.Comment: 13 page
The -extended twisted generalized Reed-Solomon code
In this paper, we give a parity check matrix for the -extended twisted
generalized Reed Solomon (in short, ETGRS) code, and then not only prove that
it is MDS or NMDS, but also determine the weight distribution. Especially,
based on Schur method, we show that the -ETGRS code is not GRS or EGRS.
Furthermore, we present a sufficient and necessary condition for any punctured
code of the -ETGRS code to be self-orthogonal, and then construct several
classes of self-dual -TGRS codes and almost self-dual -ETGRS codes
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