On self-dual mds codes
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. 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 …
On self-dual mds codes
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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 … Web19 de out. de 2024 · MDS self-dual codes have nice algebraic structures, theoretical significance and practical implications. In this paper, we present three classes of the Hermitian self-dual (extended) generalized Reed-Solomon codes with different locators. Furthermore, we showed that q^2-ary Hermitian self-dual (extended) GRS codes of …
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 … Web11 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 …
WebMaximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes … 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 …
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 … sig 320 rx opticWeb13 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 … the preferred realty intranetWeb23 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 … sig 320 specter comp for saleWeb26 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. … sig 320 x compact for saleWeb13 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 … sig 320 x5 legion opticWeb27 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] … the preferred reporting itemsWeb13 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 … sig 320 x compact pro