Factoring polynomials over Z4 and over certain Galois rings

被引：8
|
作者：
Salagean, A [1 ]
机构：
[1] Univ Loughborough, Dept Comp Sci, Loughborough LE11 3TU, Leics, England
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2005年 / 11卷 / 01期
关键词：
polynomial factoring; Galois rings; cyclic codes over rings;
D O I：
10.1016/j.ffa.2004.05.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is known that univariate polynomials over finite local rings factor uniquely into primary pairwise coprime factors. primary polynomials are not necessarily irreducible. Here we describe a factorisation into irreducible factors for primary polynomials over Z(4) and more generally over Galois rings of characteristic p(2). An algorithm is also given. As an application, we factor x(n) - 1 and x(n) + 1 over such rings. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：56 / 70
页数：15
相关论文
共 50 条
  • [31] Abelian codes over Galois rings closed under certain permutations
    Kiran, T
    Rajan, BS
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (09) : 2242 - 2253
  • [32] Binary images of cyclic codes over Z4
    Wolfmann, J
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (05) : 1773 - 1779
  • [33] DUADIC CODES OVER Z4 + uZ4
    Kumar, Raj
    Bhaintwal, Maheshanand
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2020, : 404 - 417
  • [34] Cyclic codes over Z4 + uZ4
    Bandi, Rama Krishna
    Bhaintwal, Maheshanand
    2015 SEVENTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA), 2015, : 47 - 51
  • [35] The depth spectrum of negacyclic codes over Z4
    Kai, Xiaoshan
    Wang, Lingrong
    Zhu, Shixin
    DISCRETE MATHEMATICS, 2017, 340 (03) : 345 - 350
  • [36] Near-MDR Codes over Z4
    ZHANG Xiaoyan
    MAO Qili
    Wuhan University Journal of Natural Sciences, 2014, 19 (01) : 79 - 83
  • [37] Double circulant LCD codes over Z4
    Shi, Minjia
    Huang, Daitao
    Sok, Lin
    Sole, Patrick
    FINITE FIELDS AND THEIR APPLICATIONS, 2019, 58 : 133 - 144
  • [38] Cyclic codes over a linear companion of Z4
    Udaya, P
    Bonnecaze, A
    1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 398 - 398
  • [39] Algebraic decoding of negacyclic codes over Z4
    Byrne, Eimear
    Greferath, Marcus
    Pernas, Jaume
    Zumbraegel, Jens
    DESIGNS CODES AND CRYPTOGRAPHY, 2013, 66 (1-3) : 3 - 16
  • [40] Factoring polynomials over finite fields
    Ozdemir, Enver
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2021, 17 (07) : 1517 - 1536
12345