On self-dual mds codes

Author: hcks

August undefined, 2024

WebTwisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are non-equivalent to … Web1 de mar. de 2024 · Many optimal Hermitian self-dual codes over large finite fields with new parameters are obtained. More precisely MDS or almost MDS Hermitian self-dual codes of lengths up to 18 are constructed over finite fields F q, where q = 3 2, 4 2, 5 2, 7 2, 8 2, 9 2, 11 2, 13 2, 17 2, 19 2. Comparisons with classical constructions are made.

On the Constructions of MDS Self-dual Codes via Cyclotomy

WebSelf-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS codes are very important in coding theory and practice. Thus, it is interesting to … Web13 de nov. de 2024 · In this paper we present a series of MDS self-dual codes with new length by using generalized Reed-Solomon codes and extended generalized Reed … how does the moon phases work

MDS, Near-MDS or 2-MDS Self-Dual Codes via Twisted …

Web25 de abr. de 2024 · It is proved that there is no 2 × 2 antiorthogonal matrix over G R ( 2 m , r ) with m ≥ 2 and odd r. In this study, we explore maximum distance separable (MDS) self-dual codes over Galois rings G R ( p m , r ) with p ≡ − 1 ( mod 4 ) and odd r. Using the building-up construction, we construct MDS self-dual codes of length four and eight … WebWe consider the problem for which lengths a self-dual MDS code over F q exists.We show that for q = 2 m, there are self-dual MDS codes for all even lengths up to 2 m.Furthermore, self-dual MDS codes of length q + 1 over F q exist for all odd prime powers q. Additionally, we present some new self-dual MDS codes. WebIn this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over how does the moon revolve around earth

Constructions of optimal Hermitian self-dual codes from unitary ...

Information Free Full-Text MDS Self-Dual Codes and …

Web12 de nov. de 2024 · It seems more challenging to construct self-dual NMDS codes than self-dual MDS codes. The only work on construction of self-dual NMDS codes shows existence of q-ary self-dual NMDS codes of length q - 1 for odd prime power q or length up to 16 for some small primes q with q ≤ 197. In this paper, we make use of properties of … Web1 de jan. de 2012 · MDS self-dual [18, 9, 10] codes over Fp are also constructed for p = 53, 61, 73, 89, 97., he has been with the Department of Mathematical Sciences, Yamagata … how does the moon waxes and wanes each cycleWeb23 de jun. de 2016 · This paper constructs MDS Euclidean self-dual codes which are extended cyclic duadic codes from generalized Reed-Solomon codes and constacyclic codes, and gives some results on Hermitian self- dual codes, which are the extended cyclo-duadic codes. In this paper, we construct MDS Euclidean self-dual codes which … how does the motability car scheme work

"Web12 de nov. de 2024 · It seems more challenging to construct self-dual NMDS codes than self-dual MDS codes. The only work on construction of self-dual NMDS codes shows … " - On self-dual mds codes

On self-dual mds codes

MDS or NMDS self-dual codes from twisted generalized Reed

Web11 de ago. de 2008 · MDS (selfdual) linear codes exist in a very restricted condition on their lengths as the famous MDS conjecture states: for every linear [n, k, n − k + 1] MDS … WebThis paper is organized as follows. In Section 2, we present basic facts regarding Galois rings, linear codes over , MDS codes, self-dual codes, and building-up construction. In Section 3, we discuss MDS self-dual codes over with and odd r, and we give our computational results for those codes. Specifically, we construct MDS self-dual codes …

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Webself-dual). For the study of self-dual codes, the reader is referred to [38]. The weight distribution of a code is the sequence of integers A i sfori = 0,1,...,n, where Ai is the … Web13 de jul. de 2024 · Furthermore, our general constructions provide many MDS self-dual codes with new parameters which, to the best of our knowledge, were not reported …

Web13 de nov. de 2024 · Download PDF Abstract: MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual codes with new length by using generalized Reed-Solomon codes and … Web26 de ago. de 2008 · Abstract: We construct new MDS or near-MDS self-dual codes over large finite fields. In particular, we show that there exists a Euclidean self-dual MDS …

Web1 de set. de 2024 · Since MDS self-dual codes over finite field of even characteristic with any possible parameter have been found in .In this paper, we obtain some new results on the existence of MDS self-dual codes through (extended) GRS codes over finite fields of odd characteristic. Some results in this paper extend those of and .Comparing to …

WebSimilarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts, as well as those of the previously proposed coded and colluding QPIR schemes. This is enabled by considering the stabilizer formalism and weakly self-dual generalized Reed--Solomon (GRS) star product codes.

Web1 de jan. de 2024 · In Section 3, we present our general results on the constructions of MDS self-dual codes over F q by using cyclotomic classes of F q ⁎. Then we show several … how does the moon\u0027s gravity affect tidesWebself-dual). For the study of self-dual codes, the reader is referred to [38]. The weight distribution of a code is the sequence of integers A i sfori = 0,1,...,n, where Ai is the number of codewords of weight i. A code is Euclidean (resp. Hermitian) formally self-dual (FSD) if it has the same weight distribution as its dual code with respect photocurrent-potential curvesWeb26 de fev. de 2024 · In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed–Solomon codes over finite fields of odd characteristic. … photod carleton 2 bathroomWeb8 de abr. de 2024 · In this paper, we develop a general method for constructing linear codes with small hulls using the eigenvalues of the generator matrices. Using this method, we … how does the mosfet differ from the jfet mcqWeb6 de jul. de 2008 · On self-dual MDS codes. M. Grassl, T. Gulliver. Published 6 July 2008. Computer Science. 2008 IEEE International Symposium on Information Theory. We … how does the moreton bay fig tree surviveWeb27 de jul. de 2024 · Since MDS self-dual codes over finite field of even characteristic with any possible parameter have been found in [References].In this paper, we obtain some new results on the existence of MDS self-dual codes through (extended) G R S codes over finite fields of odd characteristic. Some results in this paper extend those of [References] … photocurrent vs intensity graphWeb11 de jul. de 2008 · On self-dual MDS codes. Abstract: We consider the problem for which lengths a self-dual MDS code over F q exists.We show that for q = 2 m , there are self-dual MDS codes for all even lengths up to 2 m . Furthermore, self-dual MDS codes of length … how does the morrowseer die in wings of fire