Solomon W. Golomb

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which is equivalent to a result of Price [9], who has derived a number of expressions for these and related integrals. Note that the derivation above is, thus far, much simpler and more straightforward than the admirably executed tours de force of previous derivations. However, the last step, viz., recognizing the form of the result, is automatically(More)
Thus, if ai,,j, = ail,il= ajl,j, = aiJqj4 = 1 in the matrix, we must not have ii2 1 il 3jjL;$) = (i4 4 ,.i, -jd, nor may we have (iz i,,j, -j,)= . ,. . 13 ‘2, 3 Such matri& have been called either Costas Arrays or constellations in Ref. [2], which explores constructions as well as applications for these patterns. It is convenient to represent these arrays(More)
In this correspondence, we present a new construction for 64-QAM Golay sequences of length n=2/sup m/ for integer m. The peak envelope power (PEP) of 64-QAM Golay sequences is shown to be bounded by 4.66n. The new construction of 64-QAM Golay sequences of length n=2/sup m/ is based on our earlier construction of new offsets of 16-QAM Golay sequences which(More)
DES can be regarded as a nonlinear feedback shift register (NLFSR) with input. From this point of view, the tools for pseudo-random sequence analysis are applied to the S-boxes in DES. The properties of the S-boxes of DES under Fourier transform, Hadamard transform, extended Hadamard transform and Avalanche transform are investigated. Two important results(More)
A generalized Barker sequence is a finite sequence { ur ] of complex numbers having absolute value 1, and possessing a correlation function C(T) satisfying the constraint IC(r) 1 5 1, 7 # 0. Classes of transformations leaving lC(~)j invariant are exhibited. Constructions for generalized Barker sequences of various lengths and alphabet sizes are given.(More)
in the literature. Equation (16) shows that E(A)=2fl when ‘p= 8/a=4 dB. This result agrees well with the experimental findings in [7]. Also A,, as given by (18) yields numerical results which are in good agreement with the corresponding results obtained by numerical integration in [a]. This is somewhat surprising, since the two definitions of amplitude(More)
A widely used method of efftcient search is examined in detail. This examination provides the opportunity to formulate its scope and methods in their full generality. In addL tion to a general exposition of the basic process, some important refinemertts are indicated. Examples are given which illustrate the salient features of this searching process.