Galois Fields And Construction of 2k-1 Designs with Highest Resolution

Year 2010, Volume: 3 Issue: 1, 45 - 53, 30.06.2010

N. Danacıoğlu F. Z. Muluk

Abstract

Fractional factorialdesigns are commonly used in practice. In this article, the finite flelds theory and

polynomials over Galois fields were used to design 2k-1 designs with highest resolution.

Keywords

Factorial designs, Fractional factorial designs, Finite fileds, Galois field; Polynomials

Galois cisimleri ve en yüksek çözümlü 2^k-1 tasarımlarının oluşturulması

Abstract

Kesirli çok
etkenli tasarımları, uygulamada yaygın olarak kullanılmaktadır. Bu çalışmada,
sonlu cisim teorisinden, Galois cisimleri üzerindeki polinomlardan
yararlanarak, 2^k-1tasarımlarının nasıl oluşturulabileceği
gösterilmiştir.  

Keywords

Çok etkenli tasarımlar, Kesirli çok etkenli tasarımlar, sonlu cisimler, Galois cismi, polinomlar

References

• F. Çall alp, (1999), Say lar Teorisi, Ystanbul.
• N. Danac o lu, (2005), Kesirli Çok Etkenli Deneylerde Çözüm ve En Az Sapma Kavram , H.Ü. Ystatistik Bölümü Doktora Tezi.
• A. Dey, (1985), Orthogonal Fractional Factorial Designs, New Delhi, Wiley Eastern.
• J. A. Gallian, (1986), Contemporary Abstract Algebra, D.C.Health and Company.
• W. C. Huffman, V. Pless, (2003), Fundemantals of Error Correcting Codes, Cambridge University Pres.
• A. Kaya, (1988), Say lar Kuram na Giri(, Yzmir.
• A. J. Menezes, S. A. Vanstone, P. C. Oorschot van, (1997), Handbook of Applied Cryptography, CRC Pres.
• D. C. Montgomery, (1984), Design and Analysis of Experiments, Second Edition, John Wiley&Sons, NY.
• G. Pistone, M. P. Rogartin, (2007), Algebraic Statistics of Level Codings for Fractional Factorial Designs,
• Journal of Statistical Plann. and Inf.,138, 234-244. T. Shirakura, T. Suetsugu, T. Tsuji, (2002), Constructions of Main Effect Plus Two Plans for 2mFactorials,
• Journal of Statistical Plann. and Inf., 105, 405-415. S. A. Vanstone, P. C. Oorschot van, (1989), An Introduction to Error-Correcting Codes with Application,s
• Kluwer Academic Publishers. D. Wiggert, 1978, Error-Control Coding and Applications, Artech House.
• H. Xu, (2009), Algorithm construction of efficient fractional factorial designs with large sizes, Technometrics, 51,3,262-277.