On self-dual mds codes

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August undefined, 2024

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 … Web1 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 …

On the Constructions of MDS Self-dual Codes via Cyclotomy

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 … chrome pc antigo

Self-Dual Near MDS Codes from Elliptic Curves - IEEE Xplore

Web26 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. … 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 … Web11 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 … chrome pdf 转图片

An improved method for constructing formally self-dual codes …

New Construction of Maximum Distance Separable (MDS) Self …

Web23 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 … 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 … chromepatch adwareWeb11 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 … chrome pc indir

"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 … " - On self-dual mds codes

On self-dual mds codes

New MDS Self-dual Codes over Finite Fields of Odd Characteristic

Web1 de jan. de 2024 · In Theorem 3.1, we have proved that, when q ≡ 3 ( mod 4), there exists an MDS self-dual code of length n = p e + 1 where e is an odd integer. This gives a … 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 …

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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 … 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. 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 …

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 … 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.

Web12 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 …

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 … chrome password インポート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 … chrome para windows 8.1 64 bitsWeb1 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 … chrome password vulnerabilityWebIn this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over chrome pdf reader downloadWeb27 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] … chrome pdf dark mode chrome park apartmentsWeb1 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. chrome payment settings