5 research outputs found
Determination of sizes of optimal three-dimensional optical orthogonal codes of weight three with the AM-OPP restriction
In this paper, we further investigate the constructions on three-dimensional
optical orthogonal codes with the at most one optical
pulse per wavelength/time plane restriction (briefly AM-OPP -D -OOCs) by way of the corresponding designs. Several new
auxiliary designs such as incomplete holey group divisible designs and
incomplete group divisible packings are introduced and therefore new
constructions are presented. As a consequence, the exact number of codewords of
an optimal AM-OPP -D -OOC is finally determined for
any positive integers and
Semi-cyclic holey group divisible designs with block size three and applications to sampling designs and optical orthogonal codes
We consider the existence problem for a semi-cyclic holey group divisible
design of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD of
type (n,m^t). When t is odd and n\neq 8 or t is doubly even and t\neq 8, the
existence problem is completely solved; when t is singly even, many infinite
families are obtained. Applications of our results to two-dimensional balanced
sampling plans and optimal two-dimensional optical orthogonal codes are also
discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1304.328
Optimal -D -optical orthogonal codes and related equi-difference conflict avoiding codes
This paper focuses on constructions for optimal -D -optical orthogonal codes with . An upper
bound on the size of such codes is established. It relies heavily on the size
of optimal equi-difference -D -optical orthogonal codes, which is
closely related to optimal equi-difference conflict avoiding codes with weight
. The exact number of codewords of an optimal -D -optical orthogonal code is determined for , , and , or or
Maximum -cyclic holely group divisible packings with block size three and applications to optical orthogonal codes
In this paper we investigate combinatorial constructions for -cyclic
holely group divisible packings with block size three (briefly by -HGDPs).
For any positive integers with , the exact number
of base blocks of a maximum -cyclic -HGDP of type is
determined. This result is used to determine the exact number of codewords in a
maximum three-dimensional optical orthogonal code
with at most one optical pulse per spatial plane and per wavelength plane.Comment: 33 page
Semi-cyclic holey group divisible designs with block size three
In this paper we discuss the existence problem for a semi-cyclic holey group
divisible design of type (n,m^t) with block size 3, which is denoted by a
3-SCHGDD of type (n,m^t). When n=3, a 3-SCHGDD of type (3,m^t) is equivalent to
a (3,mt;m)-cyclic holey difference matrix, denoted by a (3,mt;m)-CHDM. It is
shown that there is a (3,mt;m)-CHDM if and only if (t-1)m\equiv 0 (mod 2) and
t\geq 3 with the exception of m\equiv 0 (mod 2) and t=3. When n\geq 4, the case
of t odd is considered. It is established that if t\equiv 1 (mod 2) and n\geq
4, then there exists a 3-SCHGDD of type (n,m^t) if and only if t\geq 3 and
(t-1)n(n-1)m\equiv 0 (mod 6) with some possible exceptions of n=6 and 8. The
main results in this paper have been used to construct optimal two-dimensional
optical orthogonal codes with weight 3 and different auto- and
cross-correlation constraints by the authors recently