The Weight Enumerator of Three Families of Cyclic Codes

Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their dual codes have been a subject of study for many years. However, their weight distributions are known only for a very small number of cases. In general the calculation of the weight distribution of cyclic codes is heavily based on the evaluation of some exponential sums over finite fields. Very recently, Li, Hu, Feng and Ge studied a class of $p$-ary cyclic codes of length $p^{2m}-1$, where $p$ is a prime and $m$ is odd. They determined the weight distribution of this class of cyclic codes by establishing a connection between the involved exponential sums with the spectrum of Hermitian forms graphs. In this paper, this class of $p$-ary cyclic codes is generalized and the weight distribution of the generalized cyclic codes is settled for both even $m$ and odd $m$ alone with the idea of Li, Hu, Feng, and Ge. The weight distributions of two related families of cyclic codes are also determined.Comment: 13 Pages, 3 Table

Stellar color regression: a spectroscopy based method for color calibration to a few mmag accuracy and the recalibration of Stripe 82

In this paper, we propose a spectroscopy based Stellar Color Regression (SCR) method to perform accurate color calibration for modern imaging surveys, taking advantage of millions of stellar spectra now available. The method is straightforward, insensitive to systematic errors in the spectroscopically determined stellar atmospheric parameters, applicable to regions that are effectively covered by spectroscopic surveys, and capable of delivering an accuracy of a few millimagnitudes for color calibration. As an illustration, we have applied the method to the SDSS Stripe 82 data (Ivezic et al; I07 hereafter). With a total number of 23,759 spectroscopically targeted stars, we have mapped out the small but strongly correlated color zero point errors present in the photometric catalog of Stripe 82, and improve the color calibration by a factor of 2 -- 3. Our study also reveals some small but significant magnitude dependence errors in z-band for some CCDs. Such errors are likely to be present in all the SDSS photometric data. Our results are compared with those from a completely independent test based on the intrinsic colors of red galaxies presented by I07. The comparison as well as other tests shows that the SCR method has achieved a color calibration internally consistent at a level of about 5 mmag in u-g, 3 mmag in g-r, and 2 mmag in r-i and i-z, respectively. Given the power of the SCR method, we discuss briefly the potential benefits by applying the method to existing, on-going, and up-coming imaging surveys.Comment: 17 pages, 14 figures, 3 tables, ApJ in pres

Determination of the Local Standard of Rest using the LSS-GAC DR1

We re-estimate the peculiar velocity of the Sun with respect to the local standard of rest using a sample of local stars within 600 pc of the Sun, selected from the LAMOST Spectroscopic Survey of the Galactic Anti-centre (LSS-GAC). The sample consists of 94332 FGK main-sequence stars with well-determined radial velocities and atmospheric parameters. To derive the LSR, two independent analyses are applied to the data. Firstly, we determine the solar motion by comparing the observed velocity distribution to that generated with the analytic formulism of Schonrich & Binney that has been demonstrated to show excellent agreement with rigorous torus-based dynamics modelling by Binney & McMillan. Secondly, we propose that cold populations of thin disc stars, selected by applying an orbital eccentricity cut, can be directly used to determine the LSR without the need of asymmetric drift corrections. Both approaches yield consistent results of solar motion in the direction of Galactic rotation, V_sun, that are much higher than the standard value adopted hitherto, derived from Stromgren's equation. The newly deduced values of V_sun are 1-2 km/s smaller than the more recent estimates derived from the Geneva-Copenhagen Survey sample of stars in the solar neighbourhood (within 100 pc). We attribute the small difference to the presence of several well-known moving groups in the GCS sample that, fortunately, hardly affect the LSS-GAC sample. The newly derived radial and vertical components of the solar motion agree well with the previous studies. In addition, for all components of the solar motion, the values yielded by stars of different spectral types in the LSS-GAC sample are consistent with each other, suggesting that the local disk is well relaxed and that the LSR reported in the current work is robust. Our final recommended LSR is, (U,V,W)_sun = (7.01+/-0.20, 10.13+/-0.12, 4.95+/-0.09) km/s.Comment: MNRAS accepted, 13 pages, 11 figures, 7 table

Automated identification of 2612 late-k and M dwarfs in the LAMOST commissioining data using the classification template fits

We develop a template-fit method to automatically identify and classify late-type K and M dwarfs in spectra from the LAMOST. A search of the commissioning data, acquired in 2009-2010, yields the identification of 2612 late-K and M dwarfs. The template fit method also provides spectral classification to half a subtype, classifies the stars along the dwarf-subdwarf metallicity sequence, and provides improved metallicity/gravity information on a finer scale. The automated search and classification is performed using a set of cool star templates assembled from the Sloan Digital Sky Survey spectroscopic database. We show that the stars can be efficiently classified despite shortcomings in the LAMOST commissioning data which include bright sky lines in the red. In particular we find that the absolute and relative strengths of the critical TiO and CaH molecular bands around 7000A are cleanly measured, which provides accurate spectral typing from late-K to mid-M, and makes it possible to estimate metallicities in a way that is more efficient and reliable than with the use of spectral indices or spectral-index based parameters such as zeta. Most of the cool dwarfs observed by LAMOST are found to be metal-rich dwarfs. We use a calibration of spectral type to absolute magnitude and estimate spectroscopic distances for all the stars; we also recover proper motions from the SUPERBLINK and PPMXL catalogs. Our analysis of the estimated transverse motions suggests a mean velocity and standard deviation for the UVW components of velocity to be: U=-9.8 km/s; V=-22.8 km/s; W=-7.9 km/s. The resulting values are general agreement with previous reported results, which yields confidence in our spectral classification and spectroscopic distance estimates, and illustrates the potential for using LAMOST spectra of K and M dwarfs for investigating the chemo-kinematics of the local Galactic disk and halo.Comment: 18 pages,16 figures,accepted for publication A