Studies on the distribution of the shortest linear recurring sequences

被引：0
|
作者：
Yin, Qian [1 ]
Yuan, Zhi-Yong [2 ]
Guo, Ping [1 ]
机构：
[1] Beijing Normal Univ, Image Proc & Pattern Recognit Lab, Beijing 100875, Peoples R China
[2] Wuhan Univ, Sch Comp Sci, Wuhan 430079, Peoples R China
来源：
INFORMATION SCIENCES | 2009年 / 179卷 / 14期
基金：
中国国家自然科学基金;
关键词：
Stream cipher; Matrix-representation method; Berlekamp-Massey algorithm; Distribution regulation; Shortest linear recurring sequences; SHIFT-REGISTER SYNTHESIS; STREAM CIPHERS; ALGORITHM;
D O I：
10.1016/j.ins.2009.01.042
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 distribution of the shortest linear recurrence (SLR) sequences in the Z/(p) field and over the Z/(p(e)) ring is studied. It is found that the length of the shortest linear recurrent (SLRL) is always equal to n/2, if n is even and n/2 + 1 if n is odd in the Z/(p) field, respectively. On the other hand, over the Z/(p(e)) ring, the number of sequences with length n can also be calculated. The recurring distribution regulation of the shortest linear recurring sequences is also found. To solve the problem of calculating the SLRL, a new simple representation of the Berlekamp-Massey algorithm is developed as well. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：2379 / 2389
页数：11
相关论文
共 50 条
  • [21] PRODUCTS OF LINEAR RECURRING SEQUENCES WITH MAXIMUM COMPLEXITY
    RUEPPEL, RA
    STAFFELBACH, OJ
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1987, 33 (01) : 124 - 131
  • [22] Finite linear recurring sequences and homogeneous ideals
    Althaler, J
    Dur, A
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 1996, 7 (05) : 377 - 390
  • [23] LINEAR RECURRING SEQUENCES OVER NONCOMMUTATIVE RINGS
    Cherchem, Ahmed
    Garici, Tarek
    Necer, Abdelkader
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2012, 11 (02)
  • [24] Weak and strong orders of linear recurring sequences
    Zenonas Navickas
    Minvydas Ragulskis
    Dovile Karaliene
    Tadas Telksnys
    Computational and Applied Mathematics, 2018, 37 : 3539 - 3561
  • [25] Weak and strong orders of linear recurring sequences
    Navickas, Zenonas
    Ragulskis, Minvydas
    Karaliene, Dovile
    Telksnys, Tadas
    COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (03): : 3539 - 3561
  • [26] Joint linear complexity of multisequences consisting of linear recurring sequences
    Fang-Wei Fu
    Harald Niederreiter
    Ferruh Özbudak
    Cryptography and Communications, 2009, 1 : 3 - 29
  • [27] Joint linear complexity of multisequences consisting of linear recurring sequences
    Fu, Fang-Wei
    Niederreiter, Harald
    Ozbudak, Ferruh
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2009, 1 (01): : 3 - 29
  • [28] Linear recurring sequences and subfield subcodes of cyclic codes
    Gao ZhiHan
    Fu FangWei
    SCIENCE CHINA-MATHEMATICS, 2013, 56 (07) : 1413 - 1420
  • [29] Joint linear complexity of arbitrary multisequences consisting of linear recurring sequences
    Fu, Fang-Wei
    Niederreiter, Harald
    Ozbudak, Ferruh
    FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (04) : 475 - 496
  • [30] A note on the minimal polynomial of the product of linear recurring sequences
    Çakçak, E
    FINITE FIELDS AND APPLICATIONS, 2001, : 57 - 69
12345