A Three-Valued Walsh Transform From Decimations of Helleseth-Gong Sequences

被引：8
|
作者：
Gong, Guang [1 ]
Helleseth, Tor [2 ]
Hu, Honggang [1 ,3 ]
机构：
[1] Univ Waterloo, Dept Elect & Comp Engn, Waterloo, ON N2L 3G1, Canada
[2] Univ Bergen, Dept Informat, Selmer Ctr, N-5020 Bergen, Norway
[3] Chinese Acad Sci, State Key Lab Informat Secur, Inst Software, Beijing 100190, Peoples R China
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2012年 / 58卷 / 02期
基金：
加拿大自然科学与工程研究理事会; 中国国家自然科学基金;
关键词：
Autocorrelation; cross-correlation; m-sequences; p-ary sequences; Walsh transform; CROSS-CORRELATION FUNCTION; FAMILY;
D O I：
10.1109/TIT.2011.2169297
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The Walsh transform of two-level autocorrelation sequences has played an important role in the construction of the set of sequences in which any two sequences are orthogonal. For p-ary sequences, there are only two basic classes of two-level autocorrelation sequences with no subfield structures for an arbitrary odd prime p. One is the class of p-ary m-sequences and the other is the class of p-ary Helleseth-Gong sequences. In this paper, the Walsh transform of a subclass of p-ary Helleseth-Gong sequences and the Walsh transform of their particular decimations are completely determined and are shown to be three-valued.
引用
收藏
页码：1158 / 1162
页数：5
相关论文
共 29 条
  • [1] New Perfect Sequences from Helleseth-Gong Sequences
    Wang, Yong
    Yang, Yang
    [J]. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2018, E101A (12): : 2392 - 2396
  • [2] New perfect sequences from Helleseth-Gong sequences
    Yang, Yang
    Wang, Yong
    [J]. 2017 EIGHTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA), 2017, : 112 - 116
  • [3] More Functions With Three-Valued Walsh Transform From Linear Combinations
    Wu, Yansheng
    Yue, Qin
    Li, Fengwei
    [J]. IEEE COMMUNICATIONS LETTERS, 2019, 23 (04) : 564 - 567
  • [4] Ternary m-sequences with three-valued crosscorrelation function:: Two new decimations
    Dobbertin, H
    Helleseth, T
    Kumar, V
    Martinsen, HM
    [J]. 2000 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2000, : 329 - 329
  • [5] Three Families of Monomial Functions With Three-Valued Walsh Spectrum
    Wu, Yansheng
    Yue, Qin
    Li, Fengwei
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (05) : 3304 - 3314
  • [6] Ternary m-sequences with three-valued cross-correlation function:: New decimations of Welch and Niho type
    Dobbertin, H
    Helleseth, T
    Kumar, PV
    Martinsen, H
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (04) : 1473 - 1481
  • [7] Binary Sequences With Three-Valued Cross Correlations of Different Lengths
    Luo, Jinquan
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (12) : 7532 - 7537
  • [8] A Reconstructing Method of PSWF Pulse Based on Three-valued Walsh Interpolation Functions
    Sai, Lei
    Liu, Chuanhui
    Lu, Faping
    Sai, Ting
    [J]. PROCEEDINGS OF 2019 IEEE 3RD INFORMATION TECHNOLOGY, NETWORKING, ELECTRONIC AND AUTOMATION CONTROL CONFERENCE (ITNEC 2019), 2019, : 271 - 276
  • [9] New Quaternary Sequences with Even Period and Three-Valued Autocorrelation
    Chung, Jin-Ho
    Han, Yun Kyoung
    Yang, Kyeongcheol
    [J]. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2010, E93A (01) : 309 - 315
  • [10] TERNARY PERFECT SEQUENCES WITH THREE-VALUED CROSS-CORRELATION
    Liu, Chenchen
    Zhang, Wenyi
    Yang, Yang
    [J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2022, 16 (04) : 893 - 901
123