Bases of Minimum-Weight Vectors for Codes from Designs

Authors:
S. Gao;J. D. Key
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, 29634, f1sgao@math.clemson.edu, keyj@math.clemson.eduf1;Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, 29634, f1sgao@math.clemson.edu, keyj@math.clemson.eduf1
Venue:
Finite Fields and Their Applications
Year:
1998

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Abstract

An explicit basis of incidence vectors for thep-ary code of the design of points and hyperplanes of the affine geometryAG"m(F"p) for any primepand any integerm=2 is obtained, which, as a corollary, gives a new elementary proof that this code is a generalized Reed-Muller code. In the proof a class of nonsingular matrices related to Vandermonde matrices is introduced.