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On self-dual mds codes

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 … 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 …

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

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 … 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 … sherbourne village vermont https://mixner-dental-produkte.com

An improved method for constructing formally self-dual codes …

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 … 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 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 … sherbourne v n power ltd

(PDF) NOTES ON MDS SELF-DUAL CODES - ResearchGate

Category:Construction of MDS Self-dual Codes over Finite Fields

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On self-dual mds codes

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

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 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 …

On self-dual mds codes

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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 …

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 … 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 …

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. … 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 …

Web7 de nov. 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. …

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 … sherbourne wardrobesWeb1 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 … sprint oil and gas dubaiWeb12 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 … sprint ohshc lyricsWebIn this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over sherbourne wardWebMaximum 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 … sprint official numberWebself-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 sprint official pageWebSelf-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 … sprint oil and gas careers