We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-CalderbankMoran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting numbertheoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.

We generalize the construction of Doppler-tolerant Golay complementary waveforms by PezeshkiCalderbank-Moran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.

We study the Mordell-Weil lattice E(K) of the elliptic K3 surface y = x + t − t in characteristic 11. We give an exact description of E(K) by using an embedding into a Niemeier lattice. Then we use the properties of the binary Golay code to enumerate the number of low length vectors. In particular we can compute the kissing number of this lattice (equivalently the number of integral sections) t...

In his 1961 paper, Marcel Golay showed how the search for pairs of binary sequences of length n with complementary autocorrelation is at worst a 2 3n 2 −6 problem. Andres, in his 1977 master’s thesis, developed an algorithm which reduced this to a 2 n 2 −1 search and investigated lengths up to 58 for existence of pairs. In this paper, we describe refinements to this algorithm, enabling a 2 n 2 ...

In this paper, we study ternary optimal formally self-dual codes. Bounds for the highest minimum weight are given for length up to 30 and examples of optimal formally self-dual codes are constructed. For some lengths, we have found formally self-dual codes which have a higher minimum weight than any self-dual code. It is also shown that any optimal formally self-dual [ 10,5,5] code is related t...

The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4bn/24c+ 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous ...

In this paper we describe a new method to diminish microprosodic components of fundamental frequency contours by applying weight functions linked to microprosodically classified phone combinations. For vowel segments in obstruent environments our algorithm outperforms standard smoothing algorithms like Moving-Average filtering, Savitzky-Golay filtering or MOMEL in diminishing F0 variations rela...