Cyclotomic linear codes of order 3

Author: qavi

August undefined, 2024

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 …

Fast polynomial arithmetic in homomorphic encryption with cyclo ...

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 … theoretical and applied climatology投稿

Cyclic codes from cyclotomic sequences of order four

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 ]. 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: … WebCyclotomic 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 … theoretical and applied climatology 分区

Linear complexity of cyclotomic sequences of order six and BCH …

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 … 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 … theoretical and applied climatology是几区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 ... theoretical anchoring meaning

"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: " - Cyclotomic linear codes of order 3

Cyclotomic linear codes of order 3

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 … 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.

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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 … 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 …

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. 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 .

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 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 ...

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 ...

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