Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

International market selection: Developing a model from Australian case studies

This paper develops a theory that firms seek out new country markets on the basis of expected commercial returns. These expectations depend on judgements about the attractiveness of the market and the firm's competitive position in it, which in turn are influenced by informants. It is the number and strengths of these informants that will underlie the probability of a country being identified and assessed as a new market by any firm.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

A survey of Australian consumers' attitudes towards UHT milk

A telephone survey was conducted in Melbourne and Brisbane to obtain a profile of milk consumption in Australia and determine consumers' attitudes regarding UHT milk. It was anticipated that this survey would reveal the reasons for the low level of UHT milk consumption in Australia. Pasteurised milk was the main milk type used by more than 80% of respondents. For UHT milk this figure was much lower (approximately 10%), even though two thirds of respondents had tried UHT milk. Factors that were found to influence UHT milk consumption included existing milk consumption habits, consumer perception, flavour and price. The majority of non-users of UHT milk stated habit of using other milk type as their main reason for not using UHT milk. Other reasons included poor nutritional value, poor flavour and not real/pure milk, indicating a negative consumer perception of the product. The flavour of UHT milk was identified as a problem, with nearly half of UHT milk users considering it to be worse than the flavour of pasteurised milk. However, a small proportion of UHT milk users preferred the flavour of UHT milk, with the majority of them stating that it was creamier, richer and/or stronger than the flavour of pasteurised milk. Prior to post-farmgate deregulation, price was shown to discourage consumers from using UHT milk. At the time of the survey, post-farmgate prices in Victoria were deregulated resulting in UHT milk being priced below that of pasteurised milk in some instances. This was believed to contribute to a significantly higher market share of the product in Melbourne than in Brisbane.