Binary sequences with two-level autocorrelation

We derive the values of the Fourier spectrum, a decomposition, and an achievable upper bound on the linear span, for binary sequences with two-level autocorrelation     

A note on the equivalence between strict optical orthogonal codes and difference triangle sets

Zhang (see IEEE Trans. Commun., vol.47, p.967-973, July 1999) proposed a special family of optical address codes, called strict optical orthogonal codes (S-OOCs), was proposed for fiber-optic code-division multiple-access (FO-CDMA) networks. Such codes can strictly guarantee both cross-correlation and autocorrelation functions constrained to have the value one in fully asynchronous data communications and ultra fast switching. In Zhang's work the theory and designs of S-OOC, plus several examples, comparison tables, and performance analyses were presented. In this article, we set up the equivalence between S-OOC and so-called difference triangle sets (DTS), which have been extensively studied previously. Thus, all the known constructions, bounds, and analyses for DTS can be directly applied to S-OOC.     

7200-phase generalized Barker sequences

We present 7200-phase generalized Barker sequences with lengths from 19 to 31. Also, we show the number of known M-phase generalized Barker sequences (M=7200), inequivalent under the group of “Barker-preserving transformations”. The autocorrelation values of Barker sequences are also presented     

Investigation of the saturation properties of gyroamplifiers

The saturation properties of a TE_0n gyroamplifier are investigated using a particle-in-cell numerical code. The effect of beam velocity spread is analyzed. It is found that for velocity spread of up to 5%, the reduction in efficiency can be compensated by extending the interaction length. A numerical optimization of efficiency enhancement using a tapered magnetic field was demonstrated. A change in the saturation mechanism from phase trapping to thermalization using the suggested tapering was observed     

Optimal interleaving schemes for correcting two-dimensional cluster errors

We present an elementary theory of optimal interleaving schemes for correcting cluster errors in two-dimensional digital data. It is assumed that each data page contains a fixed number of, say n, codewords with each codeword consisting of m code symbols and capable of correcting a single random error (or erasure). The goal is to interleave the codewords in the m×n array such that different symbols from each codeword are separated as much as possible, and consequently, an arbitrary error burst with size up to t can be corrected for the largest possible value of t. We show that, for any given m, n, the maximum possible interleaving distance, or equivalently, the largest size of correctable error bursts in an m×n array, is given by if n?⌈m²/2⌉, and t=m+⌊(n-⌈m²/2⌉)/m⌋ if n?⌈m²/2⌉. Furthermore, we develop a simple cyclic shifting algorithm that can provide a systematic construction of an m×n optimal interleaving array for arbitrary m and n. This extends important earlier work on the complementary problem of constructing interleaving arrays that, given the burst size t, minimize the interleaving degree, that is, the number of different codewords in a 2-D (or 3-D) array such that any error burst with given size t can be corrected. Our interleaving scheme thus provides the maximum burst error correcting power without requiring prior knowledge of the size or shape of an error burst.     

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

An exhaustive search for (1023, 511, 255)-cyclic difference sets has been conducted. A total of 10 non-equivalent (1023, 511, 255)-cyclic difference sets have been found, all of which are members of previously known or conjectured infinite families. A fast and effective autocorrelation test method was utilized that can also facilitate the testing of longer sequences.

     

Uniqueness of the generalized Barker sequence of length 6

It is proven that there is a unique generalized Barker sequence of length 6, modulo the group of Barker-preserving transformations