By Jean-Paul Allouche, Jeffrey Shallit (auth.), C. Ding, T. Helleseth, H. Niederreiter (eds.)
This booklet includes survey papers and study papers through top specialists on sequences and their functions. It discusses either the idea of sequences and their functions in cryptography, coding conception, communications platforms, numerical computation and laptop simulation. Sequences have vital functions in ranging structures, unfold spectrum verbal exchange platforms, multi-terminal method identity, code department multiply entry communications structures, international positioning structures, software program checking out, circuit trying out, desktop simulation, and circulate ciphers. The papers contained during this quantity assemble specialists from discrete arithmetic, desktop technology and communications engineering, and support to bridge advances in those various parts.
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Extra info for Sequences and their Applications: Proceedings of SETA ’98
Sample text
As a result, a quartet in position i results in i + 3 becoming a no-carry position. Since i is odd, i + 3 is even. Continuing in this way, we will obtain a series 0, i + 3, ... , of even no-carry positions. , the overlap which occurs at the largest index j,O ~ j ~ n - 3). Then j + 3 is a no-carry position. Note that j + 3 "I n as j is odd. In the remaining positions j+3,j+4, ... , n-l, 0,1, ... , i-2 there is by assumption, no overlap. Since there is a double at position i-I, this portion of the circle cannot be tiled by singles alone.
Until recently, the known cyclic (2m -1, 2m - 1 -1, 2m - 2 were the following: - 2 - 1) difference sets Singer difference sets for all m > O. GMW difference sets for composite m. Paley-Hadamard difference sets for 2m - 1 a prime. Some sporadic difference sets found by computer search. Crosscorrelation of m-sequences Let {u(t)} and {v(t)} be two sequences of period n with an alphabet of size p, where p is a prime. Then the crosscorrelation function between the two sequences is defined as 9u ,v(r) =L n-l wu(Hr)-v(t).
Consider the equation ~. P = 0 (mod q -1). Every nonzero multiple l(q -1), I = 1,2,3, ... of q-l can-be written in the form l(q - 1) = aq + b where a = (1- 1) and b = (q -1) - (l- 1). Thus the binary representation of l(q - 1) always has Hamming weight n. Also, (mod q - 1), we may identify every exponent 2n +j , j ~ 0 with 2j • Under such an identification, every multiple l(q - 1) of q - 1 reduces to the integer q - 1. 27 Ideal Autocorrelation Sequences Arising from Hyperovals o 1 2 3 4 n-l I I Fig.