On self-dual mds codes
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 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.
On self-dual mds codes
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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 … 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 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 … 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 …
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 … 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 …
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. …
razortooth 2007 full movieWebTwisted 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 … razortooth 2007 onlineWebself-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 razor tooth black and wbiteWeb27 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] … simrad gofree wifi 1 moduleWeb19 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 … simrad gofree wifiWebself-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 … razortooth atlasWebThis 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 … razortooth ark