Cyclotomic linear codes of order 3

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 … 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 ...

Cyclotomic Linear Codes of Order UXILIARY ESULTS

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 ... 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 … biwalent co to https://aulasprofgarciacepam.com

Cyclic Codes via the General Two-Prime Generalized Cyclotomic

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 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 … 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 … bi wallpaper quotes

Cyclotomic linear codes of order 3 ScholarBank@NUS

Category:Cyclic codes from cyclotomic sequences of order four

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Cyclotomic linear codes of order 3

Fast polynomial arithmetic in homomorphic encryption with cyclo ...

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 . 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...

Cyclotomic linear codes of order 3

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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 … WebAside from these three basic steps, all of the code for the GAP implementation has been created independently. In addition to characters, it can also accommo-date cyclotomic algebras, and makes use of shortcut algorithms for calculating local indices of cyclic cyclotomic algebras. One of these shortcut procedures is an alter-

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: 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 ...

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 … 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 …

WebMar 9, 2024 · Next, we propose a class of linear codes constructed from cyclotomic classes. Let the linear code be defined by ( 2) and the defining set be given as follows: …

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) … date greater than today sqlWebMar 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 ]. bi wallpapersWebThe 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] ... bi wallpapers freeWebMay 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. bi wallpapers for tabletWebVDOMDHTMLtml> 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. biwal manufacturing co incWebIn recent years, many classes of linear codes with interesting parameters have been obtained with this technique. Based on quadratic Gauss sums, the puncturing technique … biwam consultingWebIn 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. date group chat