Annals of Combinatorics 3 (1999) 71-80

Construction of Nested Balanced Block Designs, Rectangular Designs and q-ary Codes

K. Sinha1 and R.K. Mitra2

1Department of Statistics, Birsa Agricultural University, Ranchi-834006, India

2B.K.C. College, Calcutta-700035, India

Received July 20, 1998

AMS Subject Classification: 05B05

Abstract. A probability set function is interpretable as a probability distribution on binary sequences of fixed length. Cumulants of probability set functions enjoy particularly simple properties which make them more manageable than cumulants of general random variables. We derive some identities satisfied by cumulants of probability set functions which we believe to be new. Probability set functions may be expanded in terms of their cumulants. We derive an expansion which allows the construction of examples of probability set functions whose cumulants are arbitrary, restricted only by their absolute values. It is known that this phenomenon cannot occur for continuous probability distributions. Some particular examples of probability set functions are considered, and their cumulants are computed, leading to a conjecture on the upper bound of the values of cumulants. Moments of probability set functions determined by arithmetical conditions are computed in a final example.

Keywords: q-ary codes, nested BIB design

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