Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes

An optimal constant-composition or constant-weight code of weight $w$ has linear size if and only if its distance $d$ is at least $2w-1$. When $d\geq 2w$, the determination of the exact size of such a constant-composition or constant-weight code is trivial, but the case of $d=2w-1$ has been solved previously only for binary and ternary constant-composition and constant-weight codes, and for some sporadic instances. This paper provides a construction for quasicyclic optimal constant-composition and constant-weight codes of weight $w$ and distance $2w-1$ based on a new generalization of difference triangle sets. As a result, the sizes of optimal constant-composition codes and optimal constant-weight codes of weight $w$ and distance $2w-1$ are determined for all such codes of sufficiently large lengths. This solves an open problem of Etzion. The sizes of optimal constant-composition codes of weight $w$ and distance $2w-1$ are also determined for all $w\leq 6$, except in two cases.Comment: 12 page

Tax Reform and Housing

Current tax law provides tax advantages to owner-occupied housing that increase with a household's income. This well understood fact has led to periodic proposals to substitute a tax credit equal to, say, 25 percent of housing-related expenses for their current deductibility. Because all of the tax reforms considered in this paper (Hall-Rabushka, Kemp-Kasten and Bradley-Gephardt) move toward a flat rate schedule, they all will sharply reduce the tax-advantages of owner-occupied housing to higher income households relative to lower income households. In fact, our analysis suggests that all reforms will lower the price of obtaining housing services from owner-occupied housing for these households and raise it for higher-income households. The "breakeven" income at which the price of these housing services would be unchanged is about $55,000 for Kemp-Kasten and Hall-Rabushka probably$10,000 less for Bradley-Gephardt. The price of renting housing should rise under all reforms, probably by 5 to 10 percent. In combination with the decline in the price of obtaining housing services for middle and lower income households, this should give a signficant boost to homeownership. Under Kemp-Kasten, ownership rates will rise for four-member households with AGI (as renters) of under $60,000; for higher income households ownership could decline marginally. The breakeven income level is roughly$40,000 for Bradley-Gephardt and $35,000 or Hall-Rabushka.

Trading and the Tax Shelter Value of Depreciable Real Estate

For well-diversified investors in depreciable real estate, the trading decision may be made with the sole objective of maximizing the property's depreciation tax shelter net of all capital gain taxes and transaction costs.This paper develops a dynamic programming model in which the optimal trading strategies and depreciation methods of all investors in a property are simultaneously determined. The effects of inflation, depreciation, recapture and choice of depreciation method are analyzed, and the costs of suboptimal trading are measured. The model is applied to both conventional residential and commercial income properties under post-ERTA tax rules. At single digitinflation rates, properties are traded multiple times, and the costs of suboptimal trading are significant.

The Administration Tax Reform Proposal and Housing

This paper estimates the likely impact of the Administration tax reform plan on housing. Our analysis incorporates two general equilibrium impacts -- a one percentage point decline in the level of interest rates and a decrease in the property tax rate on principal residences -- and corrects errors regarding discount rates and refinancing in the basic rental model. A 7 percent increase in market rents (11 percent without the decline in interest rates) is projected. Consideration of the individual components of the Administration plan suggests that the only significant negative provisionis the cut in the personal tax rate from 0.53 (including a 6 percent state and local rate deductible at the Federal level) to 0.41. Without this cut (and the decline in interest rates which is largely attributable to the cut), market rents would fall by 6 percent. Rents rise only because rental housing is a negatively taxed asset in the sense that a tax cut lowers the supply of the asset.The general-equilibriwn effects will offset the negative direct effects -- the cut in marginal tax rates and loss of deductibility of property taxes -- on owner-occupied housing in the aggregate. However, this housing will generally be cheaper for households with incomes below $40,000 -- especially below$25,000 -- but will be more expensive for those with incomes above $60,000.This constitutes an improvement in both efficiency and equity because under current law the price of owner housing services is far lower for high income households than for low income households. Homeownership rates should increase by 2 to 3 percentage points for households with incomes below$40,000 and 1 to 2 percentage points in the aggregate.

Prospective Changes in Tax Law and the Value of Depreciable Real Estate

The Economic Recovery Tax Act of 1981 significantly reduced the taxation of income-producing properties by accelerating tax depreciation on both new and, especially, existing properties. A partial reversal of the 1981 legislation appears likely. To provide some insight into the possible effects of a decrease in tax depreciation of income-producing properties, two potential tax changes are analyzed: an increase from 15 to 20 years in the tax service lives of both new and existing properties and an increase for existing properties only. Both residential and commercial/industrial properties are considered.

Quantum Nonlocality of N-qubit W states

An experimental setup for testing quantum nonlocality of N qubits is proposed. This method is a generalization of the optical setup proposed by Banaszek and Wodkiewicz [1]. The quantum nonlocality of N qubits can be obtained through its violation of N-qubit Bell inequalities. The correlation function measured in the experiment is described by the Wigner function. The effect of inefficient detector is also considered.Comment: 5 pages and 2 figures, some errors are corrected in v