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2 results on '"Bilinear metric"'

1. Symmetric semisimple modules of group algebras over finite fields and self-dual permutation codes

Author

Fan, Yun and Jin, Ping

Subjects
*MATHEMATICAL symmetry, *MODULES (Algebra), *FINITE fields, *PERMUTATIONS, *FINITE groups, *BILINEAR forms, *ORTHOGONAL decompositions
Abstract

Abstract: A module of a finite group over a finite field with a symmetric non-degenerate bilinear form which is invariant by the group action is called a symmetric module. In this paper, a characterization of indecomposable orthogonal decompositions of symmetric semisimple modules and a criterion for the hyperbolic symmetric modules are obtained, and some applications to the self-dual permutation codes are shown. [Copyright &y& Elsevier]

Published
2012
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2. Symmetric semisimple modules of group algebras over finite fields and self-dual permutation codes

Author

Yun Fan and Ping Jin

Subjects
Discrete mathematics, Algebra and Number Theory, Triple system, Bilinear metric, Stanley symmetric function, Hyperbolic module, Complete homogeneous symmetric polynomial, Symmetric module, Cyclic permutation, Representation theory of the symmetric group, Symmetric group, Permutation code, Elementary symmetric polynomial, Ring of symmetric functions, Mathematics
Abstract

A module of a finite group over a finite field with a symmetric non-degenerate bilinear form which is invariant by the group action is called a symmetric module. In this paper, a characterization of indecomposable orthogonal decompositions of symmetric semisimple modules and a criterion for the hyperbolic symmetric modules are obtained, and some applications to the self-dual permutation codes are shown.

Published
2012
Full Text
View/download PDF

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