Cyclotomic linear codes of order 3

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August undefined, 2024

WebIn recent years, many classes of linear codes with interesting parameters have been obtained with this technique. Based on quadratic Gauss sums, the puncturing technique … WebThe first family of linear codes are extended primitive cyclic codes which are affine-invariant. The second family of linear codes are reducible cyclic codes. ... the order of G divides the order of F q. ... {0, 1, ⋯, n − 1} is a union of some q-cyclotomic cosets modulo n. We then introduce the extended primitive cyclic codes. Let G denote ...

Cyclotomic Linear Codes of Order UXILIARY ESULTS

WebApr 10, 2024 · This work provides refined polynomial upper bounds for the condition number of the transformation between RLWE/PLWE for cyclotomic number fields with up to 6 primes dividing the conductor. We also provide exact expressions of the condition number for any cyclotomic field, but under what we call the twisted power basis. Finally, from a … WebIn this correspondence, we construct twoclasses of linear codes with cyclotomic classes of order 3 and determine their weight distributions. Both classes contain optimal codes and … slowest cars in forza horizon 4

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WebIn this correspondence, two classes of cyclotomic linear codes over GF(q) of order 3 are constructed and their weight distributions are determined. The two classes are two … WebOct 1, 2024 · We derive the Singleton bound for poset codes and define the MDS poset codes as linear codes which attain the Singleton bound. In this paper, we study the basic properties of MDS poset... WebSep 1, 2013 · In this paper, three cyclotomic sequences of order four are employed to construct a number of classes of cyclic codes over GF (q) with prime length. Under … slowest cars

Cyclotomic linear codes of order 3 ScholarBank@NUS

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WebThe linear complexity of a sequence is defined as the smallest order of linear feedback shift register that can generate the whole sequence. ... Ding, C. Cyclotomic constructions of cyclic codes with length being the product of two primes. IEEE Trans. Inf. Theory 2012, 58, 2231–2236. [Google Scholar] ... WebMay 14, 2024 · cyclotomic: [adjective] relating to, being, or containing a polynomial of the form xp−1 + xp−2 + … + x + 1 where p is a prime number. software engineer salaries in floridaWebLinear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of q-ary linear codes under some certain conditions, where q is a power of a prime. The ... slowest cars in iracing

"WebMinimal Polynomials and Cyclotomic Cosets 3 3. Linear Codes: The Basics 5 4. Encoding and Decoding of Linear Codes 6 5. Cyclic Codes 9 6. Encoding and Decoding of Cyclic Codes 11 7. Conclusion 15 ... The order of a nonzero element 2F q, denoted by ord( ), is the smallest positive integer ksuch that k= 1. Lemma 1.9. (i) The order ord( ) divides ... " - Cyclotomic linear codes of order 3

Cyclotomic linear codes of order 3

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WebJan 21, 2024 · In this paper, we give some results and properties of cyclic codes and the cyclotomic classes of order r in Section 2. In Section 3, we construct some dual-containing cyclic codes over \mathbb {F}_ {q}. We also obtain the bound of minimum distance of those cyclic codes and some optimal or almost optimal cyclic codes. WebApr 10, 2024 · Abstract. This work provides refined polynomial upper bounds for the condition number of the transformation between RLWE/PLWE for cyclotomic number fields with up to 6 primes dividing the ...

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WebDec 1, 2024 · Three-weight cyclic codes and their weight distributions, Discrete Math. 339 (2) (2016) 415–427. [10] Ding C., Niederreiter H., Cyclotomic linear codes of order 3, IEEE Trans. Inf. Theory 53 (6) (2007) 2274–2277. [11] Ding C., Wang X., A coding theory construction of new systematic authentication codes, Theor. Comput. Sci. 330 (1) (2005) … WebCNVid-3.5M: Build, Filter, and Pre-train the Large-scale Public Chinese Video-text Dataset ... Preserving Linear Separability in Continual Learning by Backward Feature Projection Qiao Gu · Dongsub Shim · Florian Shkurti Multi-level Logit Distillation Ying Jin · Jiaqi Wang · Dahua Lin ... Graph Representation for Order-aware Visual ...

WebIn this correspondence, two classes of cyclotomic linear codes over GF (q) of order 3 are constructed and their weight distributions are determined. The two classes are two … WebCyclotomic linear codes of order 3 ScholarBank@NUS ScholarBank@NUS 1. Staff Staff Publications Please use this identifier to cite or link to this item: …

WebC. Ding / Finite Fields and Their Applications 23 (2013) 8–34 11 2.4. Cyclotomy Let r −1=nN for two positive integers n >1 and N >1, and let α be a ﬁxed primitive element of GF(r).DeﬁneC(N,r) i =α i αN for i =0,1,...,N −1, where αN denotes the subgroup of GF(r)∗ generatedby αN.Thecosets C(N,r) i arecalledthecyclotomic classes oforder N … WebJun 20, 2024 · Section 3 presents a class of linear codes from coset representatives of some subgroup of {\mathbb F}_ {q}^ {*}, and determines their weight distributions. In …

WebThe cyclotomic classes of order Nare deﬁned by C (N,r) i = α i αN for i= 0,1,··· ,N− 1, where hαNi denotes the subgroup of F∗ r generated by αN. In [31], Ding and Niederreiter …

WebMay 31, 2024 · Basic concepts of linear codes 2. Bounds on size of codes 3. Finite fields 4. Cyclic codes 5. BCH and Reed-Soloman codes 6. Duadic codes 7. Weight distributions 8. Designs 9. Self-dual codes 10. Some favourite self-dual codes 11. Covering radius and cosets 12. Codes over Z4 13. Codes from algebraic geometry 14. Convolutional codes 15. software engineer resume examples mitWebVDOMDHTMLtml> In this correspondence, two classes of cyclotomic linear codes over GF (q) of order 3 are constructed and their weight distributions are determined. The two classes are two-weight codes and contain optimal codes. They are not equivalent to irreducible cyclic codes in general when q > 2. software engineer salary adelaideWeb3. A Family of New Cyclic Codes Defined by Our Sequences 3.1. The Properties on the Generalized Cyclotomy with Order Two Over . In this subsection, the following lemmas … slowest car to 60 mphWebMay 29, 2007 · Abstract: In this correspondence, two classes of cyclotomic linear codes over GF (q) of order 3 are constructed and their weight distributions are determined. The two classes are two-weight codes and contain optimal codes. They are not equivalent to … In this correspondence, two classes of cyclotomic linear codes over GF(q) of … In this correspondence, two classes of cyclotomic linear codes over GF(q) of … IEEE Transactions on Informat - Cyclotomic Linear Codes of Order - IEEE Journals … IEEE Xplore, delivering full text access to the world's highest quality technical … Featured on IEEE Xplore The IEEE Climate Change Collection. As the world's … slowest cars of 2020 software engineer salary associate\u0027s degreeWebCyclotomic linear codes of order 3: Authors: Ding, C. Niederreiter, H. Keywords: Cyclotomy Gaussian periods Linear codes Strongly regular graphs Two-weight codes: Issue Date: Jun-2007: Citation: Ding, C., Niederreiter, H. (2007-06). Cyclotomic linear codes of order 3. IEEE Transactions on Information Theory 53 (6) : 2274-2277. slowest car sales monthsWebCyclotomic linear codes of order 3: dc.contributor.author: Ding, C. dc.contributor.author: Niederreiter, H. dc.date.accessioned: 2014-10-28T02:33:15Z: ... In this correspondence, … software engineer resume examples reddit