Uncoverings-by-bases for base-transitive permutation groups

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Uncoverings-by-bases for base-transitive permutation groups
An uncovering-by-bases for a group G acting on a finite set is a set U of bases for G such that any r-subset of is disjoint from at least one base in U, where r is a parameter dependent on G. They have applications in the decoding of permutation groups when used as error-correcting codes, and are closely related to covering designs. We give constructions for uncoverings-by-bases for many families of basetransitive group (i.e. groups which act transitively on their irredundant bases), including a general construction which works for any base-transitive group with base size 2, and some more specific constructions for other groups. In particular, those for the groups GL(3,q) and AGL(2,q) make use of the theory of finite fields. We also describe how the concept of uncovering-by-bases can be generalised to matroid theory, with only minor modifications, and give an example of this.
Robert F. Bailey
Added 25 Dec 2009
Updated 25 Dec 2009
Type Conference
Year 2006
Where DCC
Authors Robert F. Bailey
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