Kasami Power Functions, Permutation Polynomials and Cyclic Difference Sets

1999 ◽  
pp. 133-158 ◽  
Author(s):  
Hans Dobbertin
Keyword(s):  
Difference Sets ◽  
Permutation Polynomials ◽  
Power Functions ◽  
Cyclic Difference Sets

scholarly journals Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets

1999 ◽  
Vol 87 (1) ◽  
pp. 74-119 ◽  
Author(s):  
Ronald Evans ◽  
Henk D.L. Hollmann ◽  
Christian Krattenthaler ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Gauss Sums ◽  
Cyclic Difference Sets ◽  
Jacobi Sums

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

scholarly journals Exhaustive determination of (1023,~511,~255)-cyclic difference sets

2000 ◽  
Vol 70 (233) ◽  
pp. 357-367 ◽  
Author(s):  
Peter Gaal ◽  
Solomon W. Golomb
Keyword(s):  
Difference Sets ◽  
Cyclic Difference Sets

scholarly journals A Hybrid Technique Using Combinatorial Cyclic Difference Sets and Binomial Amplitude Tapering for Linear Sparse Array Antenna Design

2016 ◽  
Vol 5 (3) ◽  
pp. 73 ◽  
Author(s):  
E. Sandi ◽  
F. Y. Zulkifli ◽  
E. T. Rahardjo
Keyword(s):  
Communication Systems ◽  
Difference Sets ◽  
Array Antenna ◽  
Antenna Design ◽  
Hybrid Technique ◽  
Array Design ◽  
Sparse Array ◽  
Cyclic Difference Sets ◽  
Radar Systems ◽  
Measurement Results

Reducing system complexity and cost in synthesizing a sparse array antenna design is a challenging task for practical communication systems, such as radar systems and space communication. In this paper, a hybrid technique to synthesize a linear sparse array antenna design is described. This technique is developed using two methods. The first method is a combinatorial approach that applies cyclic difference sets (CDS) integers to significantly reduce the number of antenna elements. The approach and procedure used to apply the new CDS method to configure a linear sparse array, with significant reduction of the spatial antenna dimension, is described. The second method, applied to the array result of the first method, is amplitude tapering using a binomial array approach to reduce the sidelobes level (SLL). The simulation and measurement results of the sample sparse array design showed that the SLL was reduced in comparison to the sparse array design using only the combinatorial CDS method.

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