Vol. 8, No. 1, 2008

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Partitions in finite geometry and related constant composition codes

Tim Alderson and Keith E. Mellinger

Vol. 8 (2008), No. 1, 49–71
Abstract

We look at the construction of constant composition codes (CCCs) from various types of partitions in finite projective spaces. In particular, we construct robust classes of codes using regular spreads of PG(2n 1,q) and Baer subgeometry partitions of PG(2n,q2). For each class of codes, we bound the minimum distance by considering how such partitions can intersect. As such, we prove results about the intersection of regular spreads and Baer subgeometry partitions, two of the classical partitions generated by subgroups of a Singer group. In addition, we examine other partitions of objects embedded in finite projective spaces and their associated codes. In each case, we compare our codes to a code of comparable parameters that meets the Plotkin bound.

Keywords
spreads, Baer subgeometry partitions, constant composition codes
Mathematical Subject Classification 2000
Primary: 51E20, 94B60
Milestones
Received: 6 June 2007
Accepted: 23 January 2008
Authors
Tim Alderson
Keith E. Mellinger
Department of Mathematics
University of Mary Washington
1301 College Avenue
Trinkle Hall
Fredericksburg, VA 22401
United States