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Advances in Mathematics of Communications (AMC)
 

Weight distributions of a class of cyclic codes from $\Bbb F_l$-conjugates
Pages: 341 - 352, Issue 3, August 2015

doi:10.3934/amc.2015.9.341      Abstract        References        Full text (376.3K)           Related Articles

Chengju Li - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, China (email)
Qin Yue - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, China (email)
Ziling Heng - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, China (email)

1 L. Baumert, W. Mills and R. Ward, Uniform cyclotomy, J. Number Theory, 14 (1982), 67-82.       
2 N. Boston and G. McGuire, The weight distribution of cyclic codes with two zeros and zeta functions, J. Symb. Comput., 45 (2010), 723-733.       
3 A. R. Calderbank and J. M. Goethals, Three-weight codes and association schemes, Philips J. Res., 39 (1984), 143-152.       
4 A. Canteaut, P. Charpin and H. Dobbertin, Weight divisibility of cyclic codes, highly nonlinear functions on $\mathbbF_{2^m}$ and crosscorrelation of maximum-length sequences, SIAM J. Discrete Math., 13 (2000), 105-138.       
5 C. Carlet, P. Charpin and V. Zinoviev, Codes, bent functions and permutations suitable for DES-like cryptosystems, Des. Codes Cryptogr., 15 (1998), 125-156.       
6 C. Carlet, C. Ding and J. Yuan, Linear codes from perfect nonlinear mappings and their secret sharing schemes, IEEE Trans. Inf. Theory, 51 (2005), 2089-2102.       
7 P. Charpin, Cyclic codes with few weights and Niho exponents, J. Combin. Theory Ser. A, 108 (2004), 247-259.       
8 P. Delsarte, On subfield subcodes of modified Reed-Solomon codes, IEEE Trans. Inf. Theory, 21 (1975), 575-576.       
9 C. Ding, R. Fuji-Hara, Y. Fujiwara, M. Jimbo and M. Mishima, Sets of frequency hopping sequences: bounds and optimal constructions, IEEE Trans. Inf. Theory, 55 (2009), 3297-3304.       
10 C. Ding, Y. Liu, C. Ma and L. Zeng, The weight distributions of the duals of cyclic codes with two zeros, IEEE Trans. Inf. Theory, 57 (2011), 8000-8006.       
11 C. Ding and J. Yang, Hamming weights in irreducible cyclic codes, Discrete Math., 313 (2013), 434-446.       
12 C. Ding, Y. Yang and X. Tang, Optimal sets of frequency hopping sequences from linear cyclic codes, IEEE Trans. Inf. Theory, 56 (2010), 3605-3612.       
13 K. Feng and J. Luo, Weight distribution of some reducible cyclic codes, Finite Fields Appl., 14 (2008), 390-409.       
14 T. Feng, On cyclic codes of length $2^{2^r}-1$ with two zeros whose dual codes have three weights, Des. Codes Cryptogr., 62 (2012), 253-258.       
15 T. Feng and K. Momihara, Evaluation of the weight distribution of a class of cyclic codes based on index 2 Gauss sums, IEEE Trans. Inf. Theory, 59 (2013), 5980-5984.       
16 É. Fouvry and J. Klüners, On the 4-rank of class groups of quadratic number fields, Invent. Math., 167 (2007), 455-513.       
17 C. Li, N. Li, T. Helleseth and C. Ding, The weight distributions of several classes of cyclic codes from APN monomials, IEEE Trans. Inf. Theory, 60 (2014), 4710-4721.       
18 C. Li and Q. Yue, Weight distribution of two classes of cyclic codes with respect to two distinct order elements, IEEE Trans. Inf. Theory, 60 (2014), 296-303.       
19 C. Li, Q. Yue and F. Li, Hamming weights of the duals of cyclic codes with two zeros, IEEE Trans. Inf. Theory, 60 (2014), 3895-3902.       
20 C. Li, Q. Yue and F. Li, Weight distributions of cyclic codes with respect to pairwise coprime order elements, Finite Fields Appl., 28 (2014), 94-114.       
21 S. Li, S. Hu, T. Feng and G. Ge, The weight distribution of a class of cyclic codes related to Hermitian forms graphs, IEEE Trans. Inf. Theory, 59 (2013), 3064-3067.       
22 R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley Publishing Inc., 1983.       
23 J. Luo and K. Feng, On the weight distribution of two classes of cyclic codes, IEEE Trans. Inf. Theory, 54 (2008), 5332-5344.       
24 J. Luo, Y. Tang and H. Wang, Cyclic codes and sequences: the generalized Kasami case, IEEE Trans. Inf. Theory, 56 (2010), 2130-2142.       
25 C. Ma, L. Zeng, Y. Liu, D. Feng and C. Ding, The weight enumerator of a class of cyclic codes, IEEE Trans. Inf. Theory, 57 (2011), 397-402.       
26 G. McGuire, On three weights in cyclic codes with two zeros, Finite Fields Appl., 10 (2004), 97-104.       
27 G. Myerson, Period polynomials and Gauss sums for finite fields, Acta Arith., 39 (1981), 251-264.       
28 G. Vega, Two-weight classes cyclic codes constructed as the direct sum of two one-weight cyclic codes, Finite Fields Appl., 14 (2008), 785-797.       
29 G. Vega, The weight distribution of an extended class of reducible cyclic codes, IEEE Trans. Inf. Theory, 58 (2012), 4862-4869.       
30 G. Vega and J. Wolfmann, New classes of 2-weight cyclic codes, Des. Codes Cryptogr., 42 (2007), 327-344.       
31 B. Wang, C. Tang, Y. Qi, Y. Yang and M. Xu, The weight distributions of cyclic codes and elliptic curves, IEEE Trans. Inf. Theory, 58 (2012), 7253-7259.       
32 L. Xia and J. Yang, Cyclotomic problem, Gauss sums and Legendre curve, Sci. China Math., 56 (2013), 1485-1508.       
33 M. Xiong, The weight distributions of a class of cyclic codes, Finite Fields Appl., 18 (2012), 933-945.       
34 M. Xiong, The weight distributions of a class of cyclic codes II, Des. Codes Cryptogr., 72 (2014), 511-528.       
35 M. Xiong, The weight distributions of a class of cyclic codes III, Finite Fields Appl., 21 (2013), 84-96.       
36 J. Yang, M. Xiong, C. Ding and J. Luo, Weight distribution of a class of cyclic codes with arbitrary number of zeros, IEEE Trans. Inf. Theory, 59 (2013), 5985-5993.       
37 J. Yuan, C. Carlet and C. Ding, The weight distribution of a class of linear codes from perfect nonlinear functions, IEEE Trans. Inf. Theory, 52 (2006), 712-717.       
38 J. Yuan and C. Ding, Secret sharing schemes from three classes of linear codes, IEEE Trans. Inf. Theory, 52 (2006), 206-212.       
39 X. Zeng, L. Hu, W. Jiang, Q. Yue and X. Cao, The weight distribution of a class of p-ary cyclic codes, Finite Fields Appl., 16 (2010), 56-73.       
40 Z. Zhou and C. Ding, A class of three-weight cyclic codes, Finite Fields Appl., 25 (2014), 79-93.       
41 Z. Zhou, C. Ding, J. Luo and A. Zhang, A family of five-weight cyclic codes and their weight enumerators, IEEE Trans. Inf. Theory, 59 (2013), 6674-6682.       

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