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On self-dual mds codes

Web6 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 … Web27 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] …

MDS Self-Dual Codes and Antiorthogonal Matrices over Galois …

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. 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. iportal together energy https://liquidpak.net

Construction of MDS Self-dual Codes over Finite Fields

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 … 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 … 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 … orbital roof ct

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Category:New MDS or Near-MDS Self-Dual Codes - IEEE Xplore

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On self-dual mds codes

New MDS or Near-MDS Self-Dual Codes - IEEE Xplore

WebIn this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over

On self-dual mds codes

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Web8 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 … 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 …

Web1 de mar. de 2024 · It is easy to see that parameters of a MDS self-dual code are completely determined by the code length. The main problem in this topic is to determine existence of q-ary MDS self-dual codes of various lengths. The problem is completely solved when q is even. This paper focuses on the case that q is odd. We generalize the … 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 …

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 … 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 …

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 …

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. iportfolio groupWeb12 de jul. de 2024 · In recent years, study of self-dual maximum distance separable (MDS) codes have attracted a lot of attention [1, 4, 11,12,13,14,15, 20, 21, 32, 33, 36].First of … iportal sharjah customWeb11 de ago. de 2024 · In recent years several constructions of new self-dual MDS codes from the generalized twisted Reed-Solomon codes were proposed. In this paper we … iportal searchWeb26 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. … iportal thuan haiWeb1 de out. de 2002 · MDS Self-Dual Codes over Large Prime Fields. S. Georgiou, C. Koukouvinos. Published 1 October 2002. Computer Science, Mathematics. Finite Fields and Their Applications. Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established … orbital rower 1215Web1 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 … ipos 2022 orthoWeb11 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 … orbital safety screen