Perfect codes and balanced generalized weighing matrices☆
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 (qd−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 minimumq-rank. The classical, more involved construction for this type of BGW-matrices is discussed for comparison, and a few monomially inequivalent examples are included.
Finite Fields and Their Applications
Perfect codes and balanced generalized weighing matrices☆.
Finite Fields and Their Applications,
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