Cyclotomic linear codes of order 3

WebApr 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 … 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 …

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 ... how many plays did marlowe write https://reiningalegal.com

Linear Codes From Some 2-Designs IEEE Transactions on …

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. 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 ... WebVDOMDHTMLtml> 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. how many plays did shakespeare act in

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Cyclotomic linear codes of order 3

Weight Distributions of a Class of Linear Codes* - ResearchGate

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: … 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 ...

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 … 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 …

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... 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] ...

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 … WebMay 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.

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 clumsy of me i meant to accuse youWebIn 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 many plays does apex haveWebFeb 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. how clumsy you are ueno-sanWebMay 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 many plays does william shakespeare writeWebThe 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 clumsy you areWebIn 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 many plays has john godber writtenWebAug 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 … how many plays in average nfl game