New classes of orthogonal designs and weighing matrices derived from near normal sequences
نویسندگان
چکیده
Directed sequences have been recently introduced and used for constructing new orthogonal designs. The construction is achieved by multiplying the length and type of suitable compatible sequences. In this paper we show that near normal sequences of length n = 4m + 1 can be used to construct four directed sequences of lengths 2m+1, 2m+1, 2m, 2m and type (4m+1, 4m+1) = (n, n) with zero NPAF. The above method leads to the construction of many large orthogonal designs. In addition, we obtain new infinite families of weighing matrices constructed by near normal sequences, such as W (156+4k, 125), W (160+4k, 144), W (200+4k, 196) and W (276 + 4k, 225) for all k ≥ 0. These families resolve the existence and construction of over 30 weighing matrices which are listed as open in the second edition of the Handbook of Combinatorial Designs.
منابع مشابه
Further results on ternary complementary sequences, orthogonal designs and weighing matrices
A set of sequences is complementary, if the sum of their periodic or nonperiodic autocorrelation function is zero. Infinite families of orthogonal designs, based on some weighing matrices of order 2n, weight 2n− k and spread σ, are constructed from two circulants matrices by using complementary sequences of zero non-periodic autocorrelation function, i.e. ternary complementary pairs. Moreover, ...
متن کاملNew infinite families of orthogonal designs constructed from complementary sequences
In this paper, we present new infinite families of three and four variable orthogonal designs based on several constructions derived from complementary sequences. The above method leads to the construction of many classes of orthogonal designs. In addition, we obtain new infinite families of weighing matrices constructed by complementary sequences, such as W (144 + 4s, 144) and W (224 + 4s, 196...
متن کاملNew Results with Near-Yang Sequences
We construct new TW-sequences, weighing matrices and orthogonal designs using near-Yang sequences. In particular we construct new OD
متن کاملNew classes of orthogonal designs constructed from complementary sequences with given spread
In this paper we present infinite families of new orthogonal designs, based on some weighing matrices of order 2n, weight 2n − k and spread σ, constructed from two circulants and directed sequences.
متن کاملNew orthogonal designs from weighing matrices
In this paper we show the existence of new orthogonal designs, based on a number of new weighing matrices of order 2n and weights 2n − 5 and 2n−9 constructed from two circulants. These new weighing matrices were constructed recently by establishing various patterns on the locations of the zeros in a potential solution, in conjunction with the power spectral density criterion. We also demonstrat...
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:
- Australasian J. Combinatorics
دوره 47 شماره
صفحات -
تاریخ انتشار 2010