2024 New mds euclidean self-orthogonal codes

New mds euclidean self-orthogonal codes

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August undefined, 2024

Weborthogonal) codes. In Section 3, we give four new families of MDS self-dual codes with ﬂexible parameters. In Section 4, we make a comparison of our results with the previous results and give some examples. In Section 5, we give two new families of MDS self-orthogonal codes and MDS almost self-dual codes. In Section 6, we conclude this paper. Web28 sep. 2024 · In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$, about $\frac{1}{8}\cdot q$ new MDS Euclidean (almost)

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Web31 mei 2024 · Our first new construction of MDS Euclidean self-dual codes (see Theorems 1 and 2) is then given when these two subsets are disjoint. Secondly, we provide a simple but useful lemma (see Lemma 5), which provides a sufficient condition such that the symmetric difference of two intersecting subsets satisfies the conditions in Lemmas 2 or 3. Web31 mrt. 2024 · Generic constructions of MDS Euclidean self-dual codes via GRS codes Ziteng Huang 1 , , Weijun Fang 2 , , , Fang-Wei Fu 3 , and Fengting Li 4 , 1. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China 2. School of Cyber Science and Technology, Shandong University, Qingdao 266237, China 3. proactive mattress system

New MDS Euclidean Self-orthogonal Codes - NASA/ADS

Websuch sets, the construction of MDS Hermitian self-orthogonal codes from projective lines, and then the non-MDS codes from other algebraic curves. Over the projective lines, we present a method for embedding an MDS Hermitian self-orthogonal AG code of dimension k into an MDS Hermitian self-orthogonal code of dimension k + 1. For some special ... WebOrthogonal designs are shown to be useful in construction of self-dual codes over large fields. In this paper, we first introduce a new array of order 12, which is suitable for any set of four amicable circulant matrices. We apply some orthogonal designs of order 12 to construct new self-dual codes over large finite fields, which lead us to the ... Web14 mei 2024 · Our main techniques in constructing Euclidean and Hermitian LCD MDS codes use some linear codes with small dimension or codimension, self-orthogonal … proactive mcdonough ga

New MDS Self-dual Codes over Finite Fields DeepAI

New MDS Euclidean Self-Orthogonal Codes - IEEE Xplore

WebNew MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square q , about 1 8 ⋅q new MDS Euclidean (almost) self-dual codes over $\F_q$ can be produced. Moreover, we can construct about 1 4 ⋅q new MDS Euclidean self-orthogonal codes with different even ... proactive md addressWeb28 sep. 2024 · New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square … proactive mcdonough

"WebNew MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$, about $\frac {1} {8}\cdot q$ new MDS Euclidean (almost) self-dual codes over $\F_q$ can be produced. " - New mds euclidean self-orthogonal codes

New mds euclidean self-orthogonal codes

Web3 sep. 2024 · New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via the criterions. In particular, among our constructions, for large square q, about 1/8·q new MDS Euclidean (almost) self-dual codes over F q can be produced. … WebStabilizer codes can be constructed from self-orthogonal classical linear codes: Theorem 1. [24, 1] Let C be a linear [n,k,d] error-correcting code over the ﬁeld Fq2 such that C⊥h ⊆ C. Then, there exists an [[n,2k −n,≥ d]]q stabilizer code. The symbol ⊥h means dual with respect to Hermitian inner product. An analogous

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Web29 aug. 2024 · Euclidean (or Hermitian) self-orthogonal codes are presented and their parameters are determined by investigating the Euclidean hulls of some primitive BCH codes. 4 View 1 excerpt New constructions of MDS self-dual and self-orthogonal codes via GRS codes Ziteng Huang, Weijun Fang, Fang-Wei Fu Computer Science ArXiv 2024 … Web30 sep. 2024 · New MDS Euclidean Self-Orthogonal Codes Semantic Scholar. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via the …

WebRecently, the construction of new MDS Euclidean self-dual codes has been widely investigated. In this paper, for square q, we utilize generalized Reed-Solomon (GRS) … Web3 mrt. 2011 · Based on these constructions, a large number of new MDS self-dual codes are given with parameters for which self-dual codes were not previously known to exist. In …

Web1 sep. 2024 · Euclidean self-dual TGRS codes have also been constructed, e.g., in [21,43]. ... ... It was shown in [33, Lemma 5] that each self-orthogonal MDS code can generate a Euclidean LCD... Web1 jan. 2006 · Moreover, we can construct about 1/4· q new MDS Euclidean self-orthogonal codes with different even lengths n and dimension n/2-1. View. Show abstract.

Web31 mrt. 2024 · Generic constructions of MDS Euclidean self-dual codes via GRS codes Ziteng Huang 1 , , Weijun Fang 2 , , , Fang-Wei Fu 3 , and Fengting Li 4 , 1. Chern …

WebIf l = K such that C ⊆ C⊥E (resp. C ⊆ C⊥H), then the code C is called Euclidean self-orthogonal (resp. Hermitian self-orthogonal). In addition, if l = K = N 2 for even N,thatis to say, C = C⊥E (resp. C = C⊥H), then the code C is Euclidean self-dual (resp. Hermitian self-dual). For the study of self-dual codes, the reader is referred ... proactive md brown countyWebExplicit Constructions of MDS Self-Dual Codes. Abstract: In this paper, we study self-dual codes over finite fields using tools from algebraic function fields in one variable. An … proactive md butler rdWebSeveral classes of Galois self-orthogonal MDS codes and related applications ∗ † Yang Li, Yunfei Su, Shixin Zhu‡, Shitao Li, Minjia Shi Abstract Let q = ph be a prime power and e be an integer with 0 ≤ e ≤ h− 1. e-Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes (e= 0) and Hermitian self-orthogonal ... proactive md as medsWebAbstract: In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this … proactive md bloomington inWeb3 sep. 2024 · There are some well-known linear codes which are also Euclidean self-dual codes, such as the [24, 12,8] 2extended binary Golay code, the [12,6,6] 3 -extended … proactive md clinic crawfordsville inWeb2 jun. 2024 · New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square … proactive md careersWebare extended cyclic duadic codes or negacyclic codes. We also construct Euclidean self-dual codes which are extended negacyclic codes. Based on these constructions, a … proactivemd before and after