Perfect Codes and Balanced Generalized Weighing Matrices☆

Authors

Dieter Jungnickel, University of Augsburg
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

7-1999

Abstract

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 (q^d−1)/(q−1) overGF(q) is a balanced generalized weighing matrix over the multiplicative group ofGF(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.

Publisher's Statement

Copyright © 1999 Academic Press. All rights reserved. Publisher’s version of record:

https://doi.org/10.1006/ffta.1999.0252

Publication Title

Finite Fields and Their Applications

Recommended Citation

Jungnickel, D., & Tonchev, V. (1999). Perfect Codes and Balanced Generalized Weighing Matrices☆. Finite Fields and Their Applications, 5(3), 294-300. http://doi.org/10.1006/ffta.1999.0252
Retrieved from: https://digitalcommons.mtu.edu/math-fp/130