The homogeneous weight partition and its character-theoretic dual

Heide Gluesing-Luerssen

doi:10.1007/s10623-015-0034-1

The homogeneous weight partition and its character-theoretic dual

Heide Gluesing-Luerssen

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1007/s10623-015-0034-1
State	Published - Apr 1 2016

Bibliographical note

Funding 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.

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

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10.1007/s10623-015-0034-1

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N2 - 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.

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The homogeneous weight partition and its character-theoretic dual

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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