计算机科学 ›› 2013, Vol. 40 ›› Issue (7): 89-92.

• 信息安全 • 上一篇    下一篇

Galois环上的不完全指数和及其在Zp2导出Kerdock序列上的应用

孙霓刚,郑红,吕猛   

  1. 常州大学信息科学与工程学院 常州213164;华东理工大学计算机科学与工程系 上海200237;常州大学信息科学与工程学院 常州213164
  • 出版日期:2018-11-16 发布日期:2018-11-16
  • 基金资助:
    本文受国家自然科学基金项目(61103172,61103115)资助

Incomplete Exponential Sums over Galois Rings and their Applications in Kerdock-code Sequences Derived from Zp2

SUN Ni-gang,ZHENG Hong and LV Meng   

  • Online:2018-11-16 Published:2018-11-16

摘要: 给出了Galois环上不完全指数和的上界,并在此基础上对Zp2导出的p元Kerdock序列的非周期自相关性进行了研究,给出了序列非周期自相关性的上界,其中p为任意奇素数。结果表明,该类序列具有极低的非周期自相关性,在密码学和通信领域具有潜在的应用价值。最后,还对序列元素的部分周期分布进行了估计。

关键词: Galois环,不完全指数和,Kerdock序列,非周期自相关性,部分周期分布 中图法分类号TP309文献标识码A

Abstract: An upper bound for the incomplete exponential sums over Galois rings was derived.Based on the incomplete exponential sums,the nontrivial upper bound for the aperiodic autocorrelation of the Kerdock-code p-ary sequences derived from Zp2was given,where p is an odd prime.The result shows that these sequences have low aperiodic autocorrelation and provide strong potential applications in communication systems and cryptography.The estimate of the partial period distributions of these sequences was also derived.

Key words: Galois ring,Incomplete exponential sums,Kerdock-code sequence,Aperiodic autocorrelation,Partial period distribution

[1] 万哲先.代数和编码[M].北京:科学出版社,1979
[2] Scholtz R A,Welch L R.GMW sequences[J].IEEE Trans.Inform.Theory,1984,30(3):548-553
[3] Klapper A,Chan A H,Goresky M.Cascaded GMW sequences[J].IEEE Trans.Inform.Theory,1993,39(1):177-183
[4] No J S.Generalization of GMW sequences and No sequences[J].IEEE Trans.Inform.Theory,1996,42(1):260-262
[5] Dai Z D.Binary sequences derived from ML-sequences over rings I:Periods and minimal polynomials[J].J.Crypt.,1990,5:193-207
[6] Kasami T.Weight distribution of Bose-Chaudhuri-Hoc-queng-hem codes[C]∥Bose R C,Dowling T A. Proceedings of the Combinatorial Mathematics and its Applications.Chapel Hill,NC:University of North Carolina Press,1969:335-357
[7] Zeng X Y,Hu L,Liu Q C,et al.Binary sequences with optimal correlations and large linear span[C]∥Proceedings of the IEEE International Conference on Communications.Istanbul,Turkey,2006:385-390
[8] Zeng X Y,Hu L,Jiang W F.A family of binary sequences with 4-valued optimal out-of-phase correlation and large linear span[J].IEICE Transaction on Fundamentals of Electronics,Communications and Computer Sciences,2006,E89-A(7):2029-2035
[9] Klapper A,Goresky M.Feedback shift registers,2-adic span,and combiners with memory[J].Journal of Cryptology,1997,10(2):111-147
[10] 赵龙,韩文报,冀会芳.一类椭圆曲线二元序列的伪随机性分析[J].计算机科学,2011,38(11):71-74
[11] Boztas S,Hammons R,Kumar P V.4-phase sequences with near-optimum correlation properties[J].IEEE Trans.Inform.Theory,1992,38:1101-1113
[12] Udaya P,Siddiqi M U.Optimal and suboptimal quadriphase sequences derived from maximal length sequences over Z4[J].J.Appl.Algebra Eng.Commun.,1998,9:161-191
[13] Tang X H,Udaya P.A note on the optimal quadriphase se-quences Families[J].IEEE Trans.Inform.Theory,2007,53(1):433-436
[14] Jiang W F,Hu L,Tang X H,et al.New optimal quadriphase sequences with larger linear span[J].IEEE Trans.Inform.Theory,2009,55(1):458-470
[15] Udaya P.Polyphase and frequency hopping sequences obtained from finite rings[D].Dept.Elec.Eng.,Indian Inst.Technol.,Kanpur,India,1992
[16] Boztas S,Kumar P V.Binary sequences with Gold-like correlation but larger linear span[J].IEEE Trans.Inform.Theory,1994,40(2):532-537
[17] Tang X H,Udaya P,Fan P Z.Generalized binary Udaya-Siddiqi sequences[J].IEEE Trans.Inform.Theory,2007,53(3):1225-1230
[18] Tang X H,Helleseth T,Hu L,et al.Two new families of optimal binary sequences obtained from quaternary sequences[J].IEEE Trans.Inform.Theory,2009,55(4):1833-1840
[19] Kumar P V,Helleseth T,Calderbank A R.An upper bound for Weil exponential sums over Galois rings and applications[J].IEEE Trans.Inform.Theory,1995,41(2):456-468
[20] Shanbhag A G,Kumar P V,Helleseth T.Upper bound for a hybrid sum over Galois rings with applications to aperiodic correlation of some q-ary sequences[J].IEEE Trans.Inform.Theory,1996,42(1):250-254
[21] Hu H G,Feng D G,Wu W L.Incomplete Exponential sums over Galois rings with applications to some binary sequences derived from Z2l[J].IEEE Trans.Inform.Theory,2006,52(5):2260-2265
[22] Lahtonen J,Ling S,Solé P,et al.Z8-Kerdock codes and pseudorandom binary sequences[J].Journal of Complexity,2004,20:318-330
[23] 孙霓刚,胡磊.一类具有极低相关性的CDMA序列[J].电子学报,2010,38(7):1525-1530
[24] 孙霓刚.大线性复杂度和低相关性的p元CDMA序列[J].计算机工程,2010,36(3):22-23
[25] Golomb S W,Gong G.Signal design for good correlation--for wireless communication,cryptography and rader[M].New York:Cambridge Univ.Press,2005
[26] Helleseth T,Kumar P V.Sequences with low correlation inHandbook of Coding Theory[M]∥Pless V S,Huffman W C,eds.vol.II,Amsterdam,The Netherlands:North-Holland,1998:1765-1853
[27] Sarwate D V.An upper bound on the aperiodic autocorrelation function for a maximal-length sequence[J].IEEE Trans.Inform.Thoery,1984,30:685-687

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!