Perfect single error-correcting codes in the Johnson Scheme

Delsarte conjectured in 1973 that there are no nontrivial pefect codes in the Johnson scheme. Etzion and Schwartz recently showed that perfect codes must be k-regular for large k, and used this to show that there are no perfect codes correcting single errors in J(n,w) for n <= 50000. In this paper we show that there are no perfect single error-correcting codes for n <= 2^250.Comment: 4 pages, revised, accepted for publication in IEEE Transactions on Information Theor

Choosing a Company's Building Design: Models for Strategic Design Decisions

Improving the linkage between real estate strategy and building design can help competitive business strategy. Differentiating building design from product design is important. Problems in making design choices derive from received paradigmatic knowledge that misrepresents the design decision processes. Architectural selection problems are explained with reference to design decision processes and dilemmas of testing the design. Because comparison is the underlying method of evaluation, the design competition is discussed as a model to evaluate the design of a company’s proposed high profile buildings in relation to corporate strategy. The Appendix describes the process and the recent and past history of competitions.

Mean and Extreme Radio Properties of Quasars and the Origin of Radio Emission

We investigate the evolution of both the radio-loud fraction (RLF) and (using stacking analysis) the mean radio-loudness of quasars. We consider how these values evolve as a function of redshift and luminosity, black hole (BH) mass and accretion rate, and parameters related to the dominance of a wind in the broad emission line region. We match the FIRST source catalog to samples of luminous quasars (both spectroscopic and photometric), primarily from the Sloan Digital Sky Survey. After accounting for catastrophic errors in BH mass estimates at high-redshift, we find that both the RLF and the mean radio luminosity increase for increasing BH mass and decreasing accretion rate. Similarly both the RLF and mean radio loudness increase for quasars which are argued to have weaker radiation line driven wind components of the broad emission line region. In agreement with past work, we find that the RLF increases with increasing luminosity and decreasing redshift while the mean radio-loudness evolves in the exact opposite manner. This difference in behavior between the mean radio-loudness and the RLF in L-z may indicate selection effects that bias our understanding of the evolution of the RLF; deeper surveys in the optical and radio are needed to resolve this discrepancy. Finally, we argue that radio-loud (RL) and radio-quiet (RQ) quasars may be parallel sequences but where only RQ quasars at one extreme of the distribution are likely to become RL, possibly through slight differences in spin and/or merger history.Comment: 55 pages, 28 figures, accepted to A