Butson Hadamard matrices with partially cyclic core
نویسندگان
چکیده
In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value −1 within LCZ.
منابع مشابه
Classifying cocyclic Butson Hadamard matrices
We classify all the cocyclic Butson Hadamard matrices BH(n, p) of order n over the pth roots of unity for an odd prime p and np ≤ 100. That is, we compile a list of matrices such that any cocyclic BH(n, p) for these n, p is equivalent to exactly one element in the list. Our approach encompasses non-existence results and computational machinery for Butson and generalized Hadamard matrices that a...
متن کاملMorphisms of Butson classes
We introduce the concept of a morphism from the set of Butson Hadamard matrices over k th roots of unity to the set of Butson matrices over l roots of unity. As concrete examples of such morphisms, we describe tensor-product-like maps which reduce the order of the roots of unity appearing in a Butson matrix at the cost of increasing the dimension. Such maps can be constructed from Butson matric...
متن کاملA note on the existence of BH(19, 6) matrices
In this note we utilize a non-trivial block approach due to M. Petrescu to exhibit a Butson-type complex Hadamard matrix of order 19, composed of sixth roots of unity. 1 A new Butson-type complex Hadamard matrix A complex Hadamard matrix H is an n × n complex matrix with unimodular entries such that HH∗ = nIn, where ∗ denotes the Hermitian adjoint and In is the identity matrix of order n. Throu...
متن کاملCocyclic Butson Hadamard matrices and Codes over Zn via the Trace Map
Over the past couple of years trace maps over Galois fields and Galois rings have been used very successfully to construct cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and subsequently to generate simplex codes over Z4,Z2s and Zp and new linear codes over Zps . Here we define a new map, the trace-like map and more generally the weighted-trace map and extend these techniques ...
متن کاملNew Linear Codes over Zps via the Trace Map
The trace map has been used very successfully to generate cocyclic complex and Butson Hadamard matrices and simplex codes over Z4 and Z2s . We extend this technique to obtain new linear codes over Zps . It is worth nothing here that these codes are cocyclic but not simplex codes. Further we find that the construction method also gives Butson Hadamard matrices of order p.
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Des. Codes Cryptography
دوره 43 شماره
صفحات -
تاریخ انتشار 2007