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

Fast polynomial arithmetic in homomorphic encryption with cyclo ...

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. 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: … how far can a boomerang fly

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

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. 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, … hidratante body shop

Cyclic Codes via the General Two-Prime Generalized Cyclotomic

Linear complexity of cyclotomic sequences of order six and BCH …

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: 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 … how far can a bullet travel horizontallyWebJun 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. how far can a building cantilever

"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 … " - Cyclotomic linear codes of order 3

Cyclotomic linear codes of order 3

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WebLinear 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 ...

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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 … 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 …

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 … 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 ...

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. 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 …

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.

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 far can a bullet travel upwardsWebIn 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 … hidratante brand collectionWebApr 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). how far can a bullet travel before it fallsWebThe 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 far can a bushfire spreadWebThe 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 … how far can a bullet travel in spaceWebIn 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 far can a bullet travel in airWebAug 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. hidratante body care