Miwako Mishima

Optimal frequency hopping sequences: a combinatorial approach

Frequency hopping multiple access (FHMA) spread-spectrum communication systems employing multiple frequency-shift keying (MFSK) as data modulation technique are investigated from a combinatorial approach. A correspondence between optimal frequency hopping (FH) sequences and partition-type difference packings is first established. By virtue of this correspondence, FHMA systems with a single optimal FH sequence each are constructed from various combinatorial structures such as affine geometries, cyclic designs, and difference families. Combinatorial recursive constructions are also presented. Many new infinite series of optimal FH sequences are thus obtained. These new FH sequences are also useful in ultra wideband (UWB) communication systems.

Sets of Frequency Hopping Sequences: Bounds and Optimal Constructions

Frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies in communication systems. Frequency hopping sequences are needed in frequency hopping code-division multiple-access (FH-CDMA) systems. In this paper, four algebraic and a combinatorial constructions of optimal sets of frequency hopping sequences with new parameters are presented, and a number of bounds on sets of frequency hopping sequences are described.

On Conflict-Avoiding Codes of Length

New improved upper and lower bounds on the maximum size of a symmetric or arbitrary conflict-avoiding code of length n = 4 m for three active users are proved. Furthermore, direct constructions for optimal conflict-avoiding codes of length n = 4 m and m equiv 2 (mod 4) for three active users are provided.

n=4m

Direct constructions for optimal conflict-avoiding codes of length

for Three Active Users

n \equiv 4 \pmod{8}

Optimal Conflict-Avoiding Codes of Even Length and Weight 3

and weight 3 are provided by bringing in a new concept called an extended odd sequence. Constructions for those odd sequences are also given in this paper. As a consequence, with previously known results, the spectrum of the size of optimal conflict-avoiding codes of even length and weight 3 is completely settled.

Note: The spectrum of 1-rotational Steiner triple systems over a dicyclic group

The spectrum of values v for which a 1-rotational Steiner triple system of order v exists over a dicyclic group is determined.

Cyclically resolvable cyclic Steiner 2-systems S(2,4,52)

All cyclically resolvable cyclic Steiner 2-systems S(2,4,52) are enumerated. Up to isomorphism, there are exactly six such 2-systems. Together with the well-known cyclically resolvable 1-rotational Steiner 2-system S(2,4,52), there exist at least seven non-isomorphic resolvable Steiner 2-systems S(2,4,52).

A series of identities for the coefficients of inverse matrices on a Hamming scheme

Abstract In this paper, a series of identities concerned with inverse matrices of a linear combination of association matrices on Hamming schemes is given, which is useful in the field of statistical design of experiments.

On the optimality of orthogonal arrays in case of correlated errors

It is well known that a two-level orthogonal array of strength 2 is universally optimum for the estimation of main effects for uncorrelated errors. In this paper, the property of orthogonal arrays which are also optimum even for correlated errors is discussed and a construction for such optimal designs is presented. Furthermore, in case when there are correlations between observations which are caused by the closeness of the assemblies (treatment combinations) of experiments, it is shown that if the design matrix is a linear orthogonal array, then the OLSE and the GLSE of main effects are uncorrelated.