On self-dual mds codes

Author: xzrd

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 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 …

New MDS self-dual codes over finite fields of odd characteristic

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

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

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 … 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 … 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 … sight to see paris tn

On the Constructions of MDS Self-dual Codes via Cyclotomy

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 … 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 … sight to sound houstonWebSimilarly 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. sight to the blind larry johnson

"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 … " - On self-dual mds codes

On self-dual mds codes

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

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 … 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 …

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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 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 …

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 … 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 …

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 … sight to the blind kjvWeb6 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 … the prime factorization of 64 isWeb23 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 … the prime factorization of gcf 18 30WebSelf-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 … the prime factorization of 81 isWeb26 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. … sight to the blind bibleWeb11 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 … sight to see optometry hampton vaWeb13 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 … sight to see vision associates