Nobuko Miyamoto

Optical orthogonal codes obtained from conics on finite projective planes

Optical orthogonal codes can be applied to fiber optical code division multiple access (CDMA) communications. In this paper, we show that optical orthogonal codes with auto- and cross-correlations at most 2 can be obtained from conics on a finite projective plane. In addition, the obtained codes asymptotically attain the upper bound on the number of codewords when the order q of the base field is large enough.

Theory & Methods: Measure of Asymmetry for Square Contingency Tables Having Ordered Categories

For the analysis of square contingency tables with nominal categories, Tomizawa and coworkers have considered measures that represent the degree of departure from symmetry. This paper proposes a measure that represents the degree of asymmetry for square contingency tables with ordered categories (instead of those with nominal categories). The measure proposed is expressed using the Cressie–Read power-divergence or Patil–Taillie diversity index, defined for the cumulative probabilities that an observation falls in row (column) category i or below and column (row) category j(> i) or above. The measure depends on the order of listing the categories. It should be useful for comparing the degree of asymmetry in several tables with ordered categories. The relationship between the measure and the normal distribution is shown.

Conditional Difference Asymmetry Model for Square Contingency Tables with Nominal Categories

This paper proposes a model, which is an extension-of-symmetry model, for square contingency tables with the same nominal row and column classifications. The model states that the absolute values of difference between the conditional probability that an observation will fall in cell (i, j) on condition that it falls in cell (i, j) or (j, i) and the conditional probability that it falls in cell (j, i) on the same condition, are constant for every i≠j. The model describes a structure of asymmetry (not symmetry), and it is applied to the data on a nominal scale. An example is given.

Power-divergence-type measure of departure from diagonals-parameter symmetry for square contingency tables with ordered categories

For the analysis of square contingency tables with ordered categories, Goodman considered the diagonals-parameter symmetry (DPS) model. This paper proposes a measure to represent the degree of departure from the DPS model. The proposed measure is expressed by applying Read and Cressie’s power-divergence or Patil and Taillie’s diversity index. The measure would be useful for comparing the degree of departure from the DPS model in several tables. Examples are given.

Marginal inhomogeneity models for square contingency tables with nominal categories

Abstract For the analysis of square contingency tables with nominal categories, this paper proposes two kinds of models that indicate the structure of marginal inhomogeneity. One model states that the absolute values of log odds of the row marginal probability to the corresponding column marginal probability for each category i are constant for every i. The other model states that, on the condition that an observation falls in one of the off-diagonal cells in the square table, the absolute values of log odds of the conditional row marginal probability to the corresponding conditional column marginal probability for each category i are constant for every i. These models are used when the marginal homogeneity model does not hold, and the values of parameters in the models are useful for seeing the degree of departure from marginal homogeneity for the data on a nominal scale. Examples are given.

Difference systems of sets and a collection of 3-subsets in a finite field of order p

A difference system of set (DSS) is a collection of t disjoint ? i -subsets Q i , 0 ? i ? t - 1 , of Z n such that every non-identity element of Z n appears at least ? times in the multiset { a - b | a ? Q i , b ? Q j , 0 ? i , j ? t - 1 , i ? j } . A DSS is regular if ? i is constant for 0 ? i ? t - 1 , and a DSS is perfect if every element of Z n is contained exactly ? times in the above multiset. In this paper, we consider a collection of 3-subsets of a finite field of a prime order p = e f + 1 to be a DSS. We present a condition for which the collection forms a regular DSS and give a lower bound on the parameter ? using cyclotomic numbers for e = 3 , 4 and 6 . For the same values of e, we also show a condition for which a collection of 3-subsets is a perfect DSS.

A construction and decomposition of orthogonal arrays with non-prime-power numbers of symbols on the complement of a Baer subplane

Fuji-Hara and Kamimura (Util Math 43:65–70, 1993) outlined a method for constructing orthogonal arrays of strength 2 on the complement of a Baer subplane, with

Difference Systems of Sets with Size 2

q(q-1)