Elsevier

Discrete Mathematics

Volume 50, 1984, Pages 179-191
Discrete Mathematics

On triple-sum-sets and two or three weights codes☆

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Abstract

We introduce and characterize triple-sum-sets which are a natural generalization of partial difference sets. The perfect 3-error-correcting Golay code and uniformly packed 2-error-correcting codes are then related to triple-sum-sets and a construction is used to obtain ‘large’ coset leaders of the first order Reed-Muller codes.

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☆

Parts of this manuscript were presented at XVIe and XVIIIe Colloque des Mathématiciens du Québec, Sherbrooke, October 17, 1981 and Montreal, October 10, 1982.

∗∗

This research was supported in part by FCAC Grants #EQ 1886 and by CRSNG Grants #A 5120.

Copyright © 1984 Published by Elsevier B.V.