New Constructions of Quaternary Hadamard Matrices

نویسندگان

  • Ji-Woong Jang
  • Sang-Hyo Kim
  • Jong-Seon No
  • Habong Chung
چکیده

In this paper, we propose two new construction methods for quaternary Hadamard matrices. By the first method, which is applicable for any positive integer n, we are able to construct a quaternary Hadamard matrix of order 2 from a binary sequence with ideal autocorrelation. The second method also gives us a quaternary Hadamard matrix of order 2 from a binary extended sequence of period 2 − 1, where n is a composite number.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New Constructions of Complete Non-cyclic Hadamard Matrices, Related Function Families and LCZ Sequences

AHadamard matrix is said to be completely non-cyclic (CNC) if there are no two rows (or two columns) that are shift equivalent in its reduced form. In this paper, we present three new constructions of CNC Hadamard matrices. We give a primary construction using a flipping operation on the submatrices of the reduced form of a Hadamard matrix. We show that, up to some restrictions, the Kronecker p...

متن کامل

New Constructions of Balanced Quasi-Cyclic Generalized Hadamard Matrices

In this paper, we define quasi-cyclic (QC) generalized Hadamard matrices and balanced QC generalized Hadamard matrices. Then we propose a new construction method for QC generalized Hadamard matrices. The proposed matrices are constructed from the balanced optimal low correlation zone (LCZ) sequence set which has correlation value −1 within low correlation zone.

متن کامل

A class of quaternary noncyclic Hadamard matrices

A normalized Hadamard matrix is said to be completely noncyclic if no two row vectors are shift equivalent in its punctured matrix (i.e., with the first column removed). In this paper we present an infinite recursive construction for completely noncyclic quaternary Hadamard matrices. These Hadamard matrices are useful in constructing low correlation zone sequences.

متن کامل

New skew-Hadamard matrices via computational algebra

In this paper we formalize three constructions for skew-Hadamard matrices from a Computational Algebra point of view. These constructions are the classical 4 Williamson array construction, an 8 Williamson array construction and a construction based on OD(16; 1, 1, 2, 2, 2, 2, 2, 2, 2), a 9-variable full orthogonal design of order 16. Using our Computational Algebra formalism in conjunction with...

متن کامل

The Quaternary Complex Hadamard Conjecture of order 2 n

ABSTRACT: In this paper, a complete construction of quaternary complex Hadamard matrices of order 2 n is obtained using the method of Sylvester construction and Williamson construction. Williamson construction has been generalized to obtain any kind of Hadamard matrices (Complex or Real Numbers). Non-equivalent family of Hadamard Matrices can be obtained using the Generalized Williamson constru...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004