Cyclotomic linear codes of order 3

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August undefined, 2024

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 … 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-

Cyclic Codes via the General Two-Prime Generalized Cyclotomic

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. 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 … how much is invisalign monthly

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

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 ... 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 … 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 … how do house bills become law

1 Cyclic Codes from Cyclotomic Sequences of Order Four - arXiv

Cyclotomic Linear Codes of Order UXILIARY ESULTS

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 … 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 ... how do house flies get into houseWebMay 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. how much is invisalign monthly with insurance

"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. " - Cyclotomic linear codes of order 3

Cyclotomic linear codes of order 3

Linear codes with few weights from cyclotomic classes and …

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:

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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 ]. 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 ...

WebFeb 28, 2024 · In this paper, we propose two constructions of codebooks based on $ p $-ary linear codes and on a hybrid character sum of a special kind of functions, respectively. With these constructions, two classes of codebooks asymptotically meeting the Welch bound are presented. Keywords: Codebook, Welch bound, linear code, permutation polynomial. WebJun 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 …

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. 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, …

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: …

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 … how much is invisalign in floridaWebDec 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) … how do house building loans workWebIn recent years, many classes of linear codes with interesting parameters have been obtained with this technique. Based on quadratic Gauss sums, the puncturing technique … how much is invisalign redditWebMay 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. how much is invisalign per monthWebLinear 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 ... how do house fires startWebMar 31, 2013 · In this paper, we always assume that p = 6 f + 1 is a prime. First, we calculate the values of exponential sums of cyclotomic classes of orders 3 and 6 over … how do house flies hatchWebThe 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 . how do house flippers find houses