Hadamard Matrices with Cocyclic Core

被引:2
|
作者
Alvarez, Victor [1 ]
Armario, Jose Andres [1 ]
Frau, Maria Dolores [1 ]
Gudiel, Felix [1 ]
Guemes, Maria Belen [2 ]
Osuna, Amparo [1 ]
机构
[1] Univ Seville, Dept Appl Math 1, Seville 41004, Spain
[2] Univ Seville, Dept Algebra, Seville 41004, Spain
关键词
Hadamard matrix; circulant matrix; cocyclic matrix; difference set;
D O I
10.3390/math9080857
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Since Horadam and de Launey introduced the cocyclic framework on combinatorial designs in the 1990s, it has revealed itself as a powerful technique for looking for (cocyclic) Hadamard matrices. Ten years later, the series of papers by Kotsireas, Koukouvinos and Seberry about Hadamard matrices with one or two circulant cores introduced a different structured approach to the Hadamard conjecture. This paper is built on both strengths, so that Hadamard matrices with cocyclic cores are introduced and studied. They are proved to strictly include usual Hadamard matrices with one and two circulant cores, and therefore provide a wiser uniform approach to a structured Hadamard conjecture.
引用
收藏
页数:14
相关论文
共 50 条
  • [31] Cocyclic Hadamard matrices from forms over finite Frobenius rings
    McGuire, Gary
    Ward, Harold N.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (07) : 1730 - 1738
  • [32] Cocyclic Butson Hadamard matrices and codes over Zn via the trace map
    Pinnawala, N.
    Rao, A.
    FINITE FIELDS AND APPLICATIONS, 2008, 461 : 213 - 228
  • [33] Rooted Trees Searching for Cocyclic Hadamard Matrices over D4t
    Alvarez, Victor
    Andres Armario, Jose
    Dolores Frau, Maria
    Gudiel, Felix
    Osuna, Amparo
    APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS, AND ERROR-CORRECTING CODES, 2009, 5527 : 204 - 214
  • [34] Cocyclic orthogonal designs and the asymptotic existence of cocyclic Hadamard matrices and maximal size relative difference sets with forbidden subgroup of size 2
    de Launey, W
    Smith, MJ
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2001, 93 (01) : 37 - 92
  • [35] Calculation of cocyclic matrices
    Flannery, DL
    JOURNAL OF PURE AND APPLIED ALGEBRA, 1996, 112 (02) : 181 - 190
  • [36] The Hadamard core of the totally nonnegative matrices
    Crans, AS
    Fallat, SM
    Johnson, CR
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 328 (1-3) : 203 - 222
  • [37] Cocyclic Hadamard codes from semifields
    Udaya, P
    Horadam, K
    2000 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2000, : 31 - 31
  • [38] A new class of ternary cocyclic Hadamard codes
    Horadam, KJ
    Udaya, P
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2003, 14 (01) : 65 - 73
  • [39] Butson Hadamard matrices with partially cyclic core
    Jang, Ji-Woong
    No, Jong-Seon
    Chung, Habong
    DESIGNS CODES AND CRYPTOGRAPHY, 2007, 43 (2-3) : 93 - 101
  • [40] A Simple Cocyclic Jacket Matrices
    Lee, Moon Ho
    Feng, Gui-Liang
    Chen, Zhu
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2008, 2008