Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 47-61 |
Number of pages | 15 |
Journal | Designs, Codes, and Cryptography |
Volume | 79 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 2016 |
Bibliographical note
Publisher Copyright:© 2015, Springer Science+Business Media New York.
Keywords
- 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