Advances and Applications in Statistics
Volume 4, Issue 1, Pages 45 - 58
(April 2004)
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REGULAR FRACTIONAL FACTORIAL DESIGNS: RESOLUTION, DEFINING RELATIONS AND BLOCKING VIA CODING THEORY
H. Evangelaras (Greece), E. Kolaiti (Greece) and C. Koukouvinos (Greece)
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Abstract: The
sn–k
regular fractional factorial designs have
a simple description in terms of linear codes.
Thus, a linear code and its dual always
provide us with regular fractional factorial
design and furthermore, give us fundamental
information about its construction, resolution
and wordlength pattern. The MacWilliams
identities help in obtaining such information
without calculating a dual code. In this paper
we discuss the relationship between linear
codes and fractional sn–k
fractional factorial designs. Furthermore,
we have searched for some generalized minimum
aberration designs with factors in two and
three levels, by applying to each design its
generalized wordlength pattern. |
Keywords and phrases: linear codes, regular fractional factorial designs, defining relation, resolution, distance distribution, wordlength pattern, generalized wordlength pattern, blocking. |
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