Cyclotomic linear codes of order 3
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, … 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.
Cyclotomic linear codes of order 3
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WebCyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer … 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 …
WebDec 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) … 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 …
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 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 …
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.
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 … high waisted shorts zipperWebLinear 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 ... slow network connection on androidWebMar 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: … slow release protein foodsWebIn recent years, many classes of linear codes with interesting parameters have been obtained with this technique. Based on quadratic Gauss sums, the puncturing technique … high waisted shorts with zipperWebIn 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. high waisted shorts with zipper on sideWebThe 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 … high waisted side slit mini skirtWebIn 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 … high waisted side tie pants