Cyclotomic linear codes of order 3

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. 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 …

Linear complexity of cyclotomic sequences of order six and BCH …

WebCyclotomic 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. 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 ... grand hyatt atlanta in buckhead ga https://tipografiaeconomica.net

Cyclic codes from cyclotomic sequences of order four

WebCyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer … 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. WebMar 9, 2024 · The construction of linear codes from cryptographic functions is an interesting problem. It is efficient to construct linear codes with good parameters from popular cryptographic functions such as perfect nonlinear functions [ 4 ], almost perfect nonlinear functions [ 22, 32 ], bent functions [ 3, 6, 29] and plateaued functions [ 26 ]. chinese food amboy road staten island

The punctured codes of two classes of cyclic codes with few weights

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Cyclotomic linear codes of order 3

Fast polynomial arithmetic in homomorphic encryption with cyclo ...

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 … 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: …

Cyclotomic linear codes of order 3

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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 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 ... 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 …

WebIn this paper, let $ q $ be a power of a prime, we construct several classes of new projective three-weight or four-weight linear codes over $ \mathbb{F}_q $ from the defining sets construction, and determine their weight distributions by using additive character sums. Especially, these codes are suitable for applications in secret sharing schemes. Web3. 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 …

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 …

WebJun 1, 2015 · A classical method of constructing a linear code over GF(q) with a t-design is to use the incidence matrix of the t-design as a generator matrix over GF(q) of the code. This approach has been extensively investigated in the literature.

WebAug 14, 2024 · In order to allow the influence of small holes on crack growth path to be investigated, the G3 specimen has an 8 mm diameter hole at a horizontal location h1 = 10.5 mm and a vertical location, v1 = 3 mm. The predicted fatigue crack growth path in both softwares is identical to the experimental path obtained by , as shown in Figure 8. grand hyatt atlanta in buckhead addressWebC. 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 … chinese food americus gaWebJun 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 … grand hyatt atlanta in buckhead yelpWebAug 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 … grand hyatt atlanta 3300 peachtree roadWebApr 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 ... grand hyatt atlanta in buckhead weddingWebIn 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 … grand hyatt atlanta in buckhead spaWebCyclotomic Linear Codes of Order Abstract: In this correspondence, two classes of cyclotomic linear codes over GF (q) of order 3 are constructed and their weight … chinese food alvin texas