The homogeneous weight on a finite Frobenius ring naturally induces a partition which is invariant under left and right multiplication by units. It is shown that the character-theoretic left-sided dual of this partition coincides with the right-sided dual, and even more, the left- and right-sided Krawtchouk coefficients coincide. An example is provided showing that this is not the case for general invariant partitions if the ring is not semisimple.
|Number of pages||15|
|Journal||Designs, Codes, and Cryptography|
|State||Published - Apr 1 2016|
Bibliographical noteFunding Information:
The author would like to thank the anonymous reviewers for their very valuable and constructive comments. They have improved the paper significantly. The author was partially supported by the National Science Foundation Grant #DMS-1210061.
© 2015, Springer Science+Business Media New York.
- Character-theoretic dual partitions
- Finite Frobenius rings
- Homogeneous weight
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Applied Mathematics