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Representation Theoretic Codes

In: Representations of Lie Algebras and Partial Differential Equations

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  • Xiaoping Xu

    (Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics
    University of Chinese Academy of Sciences, School of Mathematics)

Abstract

We study the binary and ternary orthogonal codes generated by the weight matrices of finite-dimensional modules of simple Lie algebras. The Weyl groups of the Lie algebras act on these codes isometrically. It turns out that certain weight matrices of the simple Lie algebras of types A and D generate doubly-even binary orthogonal codes and ternary orthogonal codes with large minimal distances. Moreover, we prove that the weight matrices of $$F_4$$ F 4 , $$E_6$$ E 6 , $$E_7$$ E 7 and $$E_8$$ E 8 on their minimal irreducible modules and adjoint modules all generate ternary orthogonal codes with large minimal distances.

Suggested Citation

  • Xiaoping Xu, 2017. "Representation Theoretic Codes," Springer Books, in: Representations of Lie Algebras and Partial Differential Equations, chapter 0, pages 523-554, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-6391-6_14
    DOI: 10.1007/978-981-10-6391-6_14
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