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A classification of the cosets of the Reed-Muller code $ \mathcal{R}(1,6)$

Author: James A. Maiorana
Journal: Math. Comp. 57 (1991), 403-414
MSC: Primary 94B05; Secondary 94-04, 94B35
MathSciNet review: 1079027
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Abstract: The weight distribution of a coset of a Reed-Muller code $ \mathcal{R}(1,m)$ is invariant under a large transformation group consisting of all affine rearrangements of a vector space with dimension m. We discuss a general algorithm that produces an ordered list of orbit representatives for this group action. As a by-product the procedure finds the order of the symmetry group of a coset.

With $ m = 6$ we can implement the algorithm on a computer and find that there are 150357 equivalence classes. These classes produce 2082 distinct weight distributions. Their symmetry groups have 122 different orders.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1991 American Mathematical Society