Cyclotomic linear codes of order 3

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WebCyclotomic 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, … 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 - IEEE Journals

WebThe generalized cyclotomic sequence of order 4 of period nis defined bywhere and are defined by (3) and . Here, in this paper, we treat it as a sequence over a finite field ,where . Denote the multiplicative order of lmodulo n. Let be an n-th primitive root of unity over . For the sequence defined by (15), we know Define δas follows: 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 … diary of a young girl book review

Linear codes with few weights from cyclotomic classes and weakly ...

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 … 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 … 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 … diary of a young naturalist blurb

Weight Distributions of a Class of Linear Codes* - ResearchGate

Cyclic Codes via the General Two-Prime Generalized Cyclotomic

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 … 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 ... diary of a young girl- anne frank summaryWebC. 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 … diary of a young girl pages

"WebMay 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 … " - Cyclotomic linear codes of order 3

Cyclotomic linear codes of order 3

Cyclotomic Linear Codes of Order - IEEE Journals ...

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) … 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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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: … WebJul 1, 2007 · 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 …

WebThe finite subgroups of SU2 (C) are well-known; see [Vig80, Théorème I.3.7]. Let Dn be the dihedral group of order 2n. Denote by E48 the tetrahedral group, i.e., the degree-2 central extension of S4 , and by Q4n the quaternion group of order 4n (called dicyclique in [Vig80]). We have Q4n /h±1i ∼ = Dn . WebLinear 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 ...

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. 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 ...

WebApr 15, 1998 · The autocorre- lation function of the ternary cyclotomic sequence of order 3 is given by AC, (T)=-l+ ( +l~), where s = e27'^1/3. Proof. We need results about cyclotomic numbers of order 3 which were determined by Dickson [4]. Let p = 3t + 1, then the cyclotomic numbers of order 3 are ( (,y)= ,n (Dy+l) , (,7e {0,l,2).

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 … diary of a young girl summaryWebCyclotomic 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. diary of a zulu girl free pdf downloadWebJun 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 … cities skylines remove zoning from roadWebIn 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 … diary of a young girl onlineWebApr 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 … cities skylines remove need for power linesWebThe 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 constructed two classes of cyclotomic linear codes CD¯ over Fp of order 3 with deﬁning sets D¯ = D 0 and D¯ = D 0 S D 1, where Dj = {αjα3i: i= 0,1 ... cities skylines render it profileWebAug 1, 2014 · First, we calculate the values of exponential sums of cyclotomic classes of orders 3 and 6 over an extension field of GF (3). Then, we give a formula to compute the … diary of a young naturalist extract