Results 241 to 250 of about 2,796,806 (297)
Some of the next articles are maybe not open access.
International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., 2004
An inverse relative dimension/length profile (IRDLP) of a pair of codes was introduced to describe the equivocation. In this paper, the maximum distance separable (MDS) code is extended to a two-code format: relative MDS pair. For a code and a subcode, the pair is called a relative MDS pair if its inverse relative dimension-length profile (IRDLP ...
Yuan Luo 0003 +3 more
openaire +1 more source
An inverse relative dimension/length profile (IRDLP) of a pair of codes was introduced to describe the equivocation. In this paper, the maximum distance separable (MDS) code is extended to a two-code format: relative MDS pair. For a code and a subcode, the pair is called a relative MDS pair if its inverse relative dimension-length profile (IRDLP ...
Yuan Luo 0003 +3 more
openaire +1 more source
International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., 2004
We construct maximum distance separable quantum error-correcting codes. The codes are defined over q-dimensional quantum systems, where q is any prime power. The construction yields quantum MDS codes of length up to q+1 for all possible dimensions and some quantum MDS codes of length up to q2+1.
Rötteler, M., Grassl, M., Beth, T.
openaire +1 more source
We construct maximum distance separable quantum error-correcting codes. The codes are defined over q-dimensional quantum systems, where q is any prime power. The construction yields quantum MDS codes of length up to q+1 for all possible dimensions and some quantum MDS codes of length up to q2+1.
Rötteler, M., Grassl, M., Beth, T.
openaire +1 more source
New Constructions of q-Ary MDS Array Codes With Multiple Parities and Their Effective Decoding
IEEE Transactions on Information Theory, 2023From the perspective of parity-check matrices, we present new constructions of $q$ -ary maximum distance separable (MDS) array codes with multiple parities.
Jingjie Lv +4 more
semanticscholar +1 more source
New Families of MDS Symbol-Pair Codes From Matrix-Product Codes
IEEE Transactions on Information Theory, 2023In emerging storage technologies, the outputs of the channels consist of overlapping pairs of symbols. The errors are no longer individual symbols. Controlling them calls for a different approach. Symbol-pair codes have been proposed as a solution.
Gaojun Luo +3 more
semanticscholar +1 more source
IEEE Transactions on Information Theory, 1983
Summary: Maximum distance separable (MDS) convolutional codes are defined as the row space over \(F(D)\) of totally nonsingular polynomial matrices in the indeterminate \(D\). These codes may be used to transmit information on \(n\) parallel channels when a temporary or even an infinite break can occur in some of these channels.
Philippe Piret, Thijs Krol
openaire +1 more source
Summary: Maximum distance separable (MDS) convolutional codes are defined as the row space over \(F(D)\) of totally nonsingular polynomial matrices in the indeterminate \(D\). These codes may be used to transmit information on \(n\) parallel channels when a temporary or even an infinite break can occur in some of these channels.
Philippe Piret, Thijs Krol
openaire +1 more source
Generalized GM-MDS: Polynomial Codes Are Higher Order MDS
IEEE Transactions on Information Theory, 2023The GM-MDS theorem, conjectured by Dau-Song-Dong-Yuen and proved by Lovett and Yildiz-Hassibi, shows that the generator matrices of Reed-Solomon codes can attain every possible configuration of zeros for an MDS code.
Joshua Brakensiek +2 more
semanticscholar +1 more source
New MDS entanglement-assisted quantum codes from MDS Hermitian self-orthogonal codes
Designs, Codes and Cryptography, 2022The intersection $$\textbf{C}\cap \textbf{C}^{\perp _H}$$ C ∩ C ⊥ H of a linear code $$\textbf{C} \subset \textbf{F}_{q^2}^n$$ C ⊂ F q 2 n and its Hermitian dual $$\textbf{C}^{\perp _H}$$ C ⊥ H is called the Hermitian hull of this code.
Hao Chen
semanticscholar +1 more source
Some quantum MDS codes from GRS codes
Linear and multilinear algebra, 2023The construction of quantum maximum-distance-separable (MDS) codes has become one of the major goals in quantum coding theory. In this paper, we construct several classes of Hermitian self-orthogonal generalized Reed–Solomon codes.
Guohui Wang, Chunming Tang
semanticscholar +1 more source
Designs, Codes and Cryptography, 1996
A linear \([n,k,d]\) code \(C\) over the finite field \(F_q\) is called almost maximum distance separable (AMDS for short) if its Singleton defect \(s(C) = n-k+1-d\) is one. A set of \(n\) points in the projective space \(PG(r,q)\) over \(F_q\) of dimension \(r\) is called \(n\)-track if every \(r\) of the points are not contained in a subspace of ...
openaire +1 more source
A linear \([n,k,d]\) code \(C\) over the finite field \(F_q\) is called almost maximum distance separable (AMDS for short) if its Singleton defect \(s(C) = n-k+1-d\) is one. A set of \(n\) points in the projective space \(PG(r,q)\) over \(F_q\) of dimension \(r\) is called \(n\)-track if every \(r\) of the points are not contained in a subspace of ...
openaire +1 more source
Annals of Combinatorics, 2005
An MDS code over an alphabet of size \(q\) is a set of length \(n\) vectors with \(q^k\) elements where the minimum distance \(d\) satisfies \(d=n-k+1.\) Any MDS code satisfies the bound \(n \leq q+k-1.\) If equality is met in this bound the code is said to be of maximal length.
openaire +1 more source
An MDS code over an alphabet of size \(q\) is a set of length \(n\) vectors with \(q^k\) elements where the minimum distance \(d\) satisfies \(d=n-k+1.\) Any MDS code satisfies the bound \(n \leq q+k-1.\) If equality is met in this bound the code is said to be of maximal length.
openaire +1 more source