New Optimal Binary Sequences with Period 4p4p via Interleaving Ding-Helleseth-Lam Sequences

Binary sequences with optimal autocorrelation play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation has been an interesting research topic in sequence design. Ding-Helleseth-Lam sequences are such a class of binary sequences of period $p$, where $p$ is an odd prime with $p\equiv 1(\bmod~4)$. The objective of this letter is to present a construction of binary sequences of period $4p$ via interleaving four suitable Ding-Helleseth-Lam sequences. This construction generates new binary sequences with optimal autocorrelation which can not be produced by earlier ones

On 55-manifolds with free fundamental group and simple boundary links in S5S^5

We classify compact oriented $5$-manifolds with free fundamental group and $\pi_{2}$ a torsion free abelian group in terms of the second homotopy group considered as $\pi_1$-module, the cup product on the second cohomology of the universal covering, and the second Stiefel-Whitney class of the universal covering. We apply this to the classification of simple boundary links of $3$-spheres in $S^5$. Using this we give a complete algebraic picture of closed $5$-manifolds with free fundamental group and trivial second homology group.Comment: 20 page

Interaction Between Supernova Remnant G22.7-0.2 And The Ambient Molecular Clouds

We have carried out 12CO (J=1-0 and 2-1), 13CO (J=1-0), and C18O (J=1-0) observations in the direction of the supernova remnant (SNR) G22.7-0.2. A filamentary molecular gas structure, which is likely part of a larger molecular complex with VLSR~75-79 km/s, is detected and is found to surround the southern boundary of the remnant. In particular, the high-velocity wing (77-110 km/s) in the 12CO (J=1-0 and J=2-1) emission shows convincing evidence of the interaction between SNR G22.7-0.2 and the 75-79 km/s molecular clouds (MCs). Spectra with redshifted profiles, a signature of shocked molecular gas, are seen in the southeastern boundary of the remnant. The association between the remnant and the 77 km/s MCs places the remnant at the near distance of 4.0-4.8 kpc, which agrees with a location on the Scutum-Crux arm. We suggest that SNR G22.7-0.2, SNR W41, and HII region G022.760-0.485 are at the same distance and are associated with GMC G23.0-0.4.Comment: 9 pages, 9 figures, 3 tables, accepted for publication in Ap