Hadamard Matrices of Order 28m, 36m and 44m
نویسنده
چکیده
We show that if four suitable matrices of order m exist then there are Hadamard matrices of order 28 m, 36 m, and 44 m. In particular we show that Hadamard matrices of orders 14(q + 1), 18(q + 1), and 22(q + 1) exist when q is a prime power and q = l(mod 4). Also we show that if n is the order of a conference matrix there is an Hadamard matrix of order 4mn. As a consequence there are Hadamard matrices of the following orders less than 4000: 476, 532, 836, 1036, 1012, 1100, 1148, 1276, 1364, 1372, 1476, 1672, 1836,2024, 2052, 2156, 2212, 2380, 2484, 2508, 2548, 2716, 3036, 3476, 3892. All these orders seem to be new. Disciplines Physical Sciences and Mathematics Publication Details Jennifer Seberry Wallis, Hadamard matrices of order 28m, 36m, and 44m, Journal of Combinatorial Theory, Ser. A., 15, (1973), 323-328. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/951 Reprinted from JOURNAL OF COMBINATORIAL THEORY All Rights Reserved by Academic Press, New York and London Note Vol. 15, No.3, November 1973 Printed in Belgium Hadamard Matrices of Order 28m, 36m and 44m
منابع مشابه
Weak log-majorization inequalities of singular values between normal matrices and their absolute values
This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$. Some applications to these inequalities are also given. In addi...
متن کاملOn the classification of Hadamard matrices of order 32
All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of inequivalent Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13,680,757 Hadamard matrices of one type and 26,369 such matrices of another t...
متن کاملThe cocyclic Hadamard matrices of order less than 40
In this paper all cocyclic Hadamard matrices of order less than 40 are classified. That is, all such Hadamard matrices are explicitly constructed, up to Hadamard equivalence. This represents a significant extension and completion of work by de Launey and Ito. The theory of cocyclic development is discussed, and an algorithm for determining whether a given Hadamard matrix is cocyclic is describe...
متن کاملON DESIGNS CONSTRUCTED FROM HADAMARD MATRICES SHOAIB UD DIN and V. C. MAVRON
There is a well-known correspondence between symmetric 2-(4ju— 1,2/z — 1,/z — 1) designs and Hadamard matrices of order 4^. It is not so well known that there is a natural correspondence between Hadamard matrices of order 2\x and affine l-(4ju, 2^, 2(i) designs whose duals are also affine. Such a design is denoted by H^fi) in this paper. Under this natural correspondence, two H^fi) designs are ...
متن کاملThe Product of Four Hadamard Matrices
We prove that if there exist Hadamard matrices of order 4m, 4n, 4p, 4q then there exists an Hadamard matrix of order 16mnpq. This improves and extends the known result of Agayan that there exists an Hadamard matrix of order 8mn if there exist Hadamard matrices of order 4m and 4n.
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:
- J. Comb. Theory, Ser. A
دوره 15 شماره
صفحات -
تاریخ انتشار 1973