On generator matrices of MDS codes (Corresp.)

Roth, Ron M.; Seroussi, G.

doi:10.1109/tit.1985.1057113

Cited by 98 publications

(102 citation statements)

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“…Superregular matrices with entries in a finite field can be obtained from Cauchy matrices or Vandermonde matrices (see, for example, [15,16,19,20]). …”

Section: Resultsmentioning

confidence: 99%

“…Theorem 1 (Proposition 3.2 of [14] Recall that matrix is said to be superregular (see [15]) if every square submatrix is nonsingular. Several constructions of MDS block codes based on superregular matrices have been proposed (see, for example, [15,16]). Our purpose here is to extend these constructions using the characterization given in Theorem 1 in order to obtain linear array codes which are also MDS.…”

Section: Preliminariesmentioning

confidence: 99%

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A construction of MDS array codes

Cardell

Climent

Requena

2013

WIT Transactions on Information and Communication Technologies

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“…Superregular matrices with entries in a finite field can be obtained from Cauchy matrices or Vandermonde matrices (see, for example, [15,16,19,20]). …”

Section: Resultsmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

A construction of MDS array codes

Cardell

Climent

Requena

2013

WIT Transactions on Information and Communication Technologies

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“…First, we use a k × (k + m)-systematic generator matrix built from a k × k-identity matrix concatenated to a k × m Generalized Cauchy (GC) matrix [10]. A GC matrix generates a systematic MDS code and it contains only 1 on its first row and on its first column.…”

Section: Application Of Transformsmentioning

confidence: 99%

Polynomial ring transforms for efficient XOR-based erasure coding

Detchart

Lacan

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Abstract-The complexity of software implementations of MDS erasure codes mainly depends on the efficiency of the finite field operations implementation. In this paper, we propose a method to reduce the complexity of the finite field multiplication by using simple transforms between a field and a ring to perform the multiplication in a ring. We show that moving to a ring reduces the complexity of the operations. Then, we show that this construction allows the use of simple scheduling to reduce the number of operations.

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“…Obviously all the entries of these matrices must be nonzero. Also, in [1,22], several examples of triangular matrices were constructed in such a way that all submatrices inside this triangular configuration were nonsingular. However, all these notions do not apply to our case as they do not consider submatrices that contain zeros.…”

Section: Superregular Matricesmentioning

confidence: 99%

On Optimal Extended Row Distance Profile

Almeida

Napp

Pinto

2017

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper, we investigate extended row distances of Unit Memory (UM) convolutional codes. In particular, we derive upper and lower bounds for these distances and moreover present a concrete construction of a UM convolutional code that almost achieves the derived upper bounds. The generator matrix of these codes is built by means of a particular class of matrices, called superregular matrices. We actually conjecture that the construction presented is optimal with respect to the extended row distances as it achieves the maximum extended row distances possible. This in particular implies that the upper bound derived is not completely tight. The results presented in this paper further develop the line of research devoted to the distance properties of convolutional codes which has been mainly focused on the notions of free distance and column distance. Some open problems are left for further research.

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On generator matrices of MDS codes (Corresp.)

Cited by 98 publications

References 1 publication

A construction of MDS array codes

A construction of MDS array codes

Polynomial ring transforms for efficient XOR-based erasure coding

On Optimal Extended Row Distance Profile

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