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Perfect Codes and Balanced Generalized Weighing Matrices

✍ Scribed by Dieter Jungnickel; Vladimir D. Tonchev

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 110 KB
Volume: 5
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1999.0252

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✦ Synopsis

It is proved that any set of representatives of the distinct one-dimensional subspaces in the dual code of the unique linear perfect single-error-correcting code of length (qB!1)/(q!1) over GF(q) is a balanced generalized weighing matrix over the multiplicative group of GF(q). Moreover, this matrix is characterized as the unique (up to equivalence) wieghing matrix for the given parameters with minimum q-rank. The classical, more involved construction for this type of BGW-matrices is discussed for comparison, and a few monomially inequivalent examples are included.

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