Balanced Incomplete Block Design (Bibd) Using Hadamard Rhotrices

P. L. Sharma and S. Kumar

Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla - 171005, India.

*Corresponding Author E-mail: plsharma1964@gmail.com, satishkumar31982@gamil.com.

ABSTRACT:

Hadamard matrices have received much attention in the recent past, owing to their well-known and promising applications. Various researchers have used Hadamard matrices to find their applications in image analysis, signal processing, coding theory, cryptology and combinatorial designs. Now, Hadamard rhotrices have been introduced in the literature for the above said applications. Balanced incomplete block design has its wide use in design of experiments in statistics and error-correcting codes. Design of experiments has broad applications across all the natural and social sciences, and engineering. Here, in the present paper, we develop balanced incomplete block design (BIBD) using Hadamard rhotrices.

AMS Classification: 05B05, 62K10, 20H30.

KEYWORDS: Hadamard Matrix; Hadamard Rhotrix; Incidence Matrix; Balanced Incomplete Block Design.

1. INTRODUCTION:

The famous matrix with orthogonal property was defined by Sylvester [1] in 1867 and further studied by Hadamard [2] in 1893 and now known as Hadamard matrix. Hadamard matrices have wide range of applications in different branches of mathematical sciences and other sciences. They play a vital role in theory and construction of experimental designs due to their equivalence to some block designs. Design theory has its roots in recreational mathematics. There are many designs first considered in the context of mathematical puzzles or brain-teasers in the eighteenth and nineteenth centuries. The study of design theory as a mathematical object became important due to applications in the design and analysis of statistical experiments. Designs have applications in tournament scheduling, lotteries, mathematical biology, algorithm design and analysis, group testing, and cryptography. If we wish to make sub committees from a committee having large number of members with some conditions such a system of subcommittees can be described mathematically by a balanced block design and these designs exist by suitable value of parameters.

3. CONCLUSION:

In the present paper, we have used rhotrices in designing blocks. The Hadamard rhotrix along with its coupled matrices is used to construct Balanced Incomplete Block Design which has useful applications in mathematical biology, algorithm design and analysis, group testing and cryptography.

4. REFERENCES:

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Received on 14.01.2014 Accepted on 28.01.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 62-66