Cyclotomic linear codes of order 3

Author: ilbc

August undefined, 2024

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, we construct twoclasses of linear codes with cyclotomic classes of order 3 and determine their weight distributions. Both classes contain optimal codes and …

Cyclotomic Linear Codes of Order - IEEE Journals

WebMar 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 … 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 … slw10r-5c7lf

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

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 … 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, … 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 … solar power banks australia

Applied Sciences Free Full-Text Two- and Three-Dimensional ...

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 … 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... solar powerbank stiftung warentestWebLinear 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 ... s lw + 0.5ph

"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. " - Cyclotomic linear codes of order 3

Cyclotomic linear codes of order 3

Cyclic codes from cyclotomic sequences of order four - ScienceDirect

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 constructions of cyclic codes with length being the product of two primes. IEEE Trans. Inf. Theory 2012, 58, 2231–2236. [Google Scholar] ...

Did you know?

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 ... 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:

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 ... 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: …

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. 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 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 . solar power banks for emergenciesWebCyclotomic 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 … slw11lc-bWebApr 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). slw10aWebMay 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. slw10s-1c7lfWebJun 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 … solar power bank t11wWebCNVid-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 ... solar powerbank qiWebIn 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. slw11-f