On self-dual mds codes
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. 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
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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 … 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 … 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 …
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 … 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 …
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 …
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 … chiton shell proteomeWeb25 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 … grass beater bonideWebWe 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. chiton shell plateWeb23 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 … grass beachesWeb19 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 … grass bean bag chairWebTwisted 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 … grass beaterWeb13 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 … chitons in insects