Self-Orthogonal Codes and the Topology of Spinor Groups
Maximal doubly-even self-orthogonal binary linear codes correspond to the maximal elementary abelian 2-groups of the spinor group Spin(n). We will describe the correspondence and discuss various techniques from the algebraic topology of Spin(n) which may be useful in studying self-orthogonal codes. In particular, Quillen’s results in equivariant cohomology theory coupled with some Morse theory may allow one to address certain questions on the minimum weight of doubly-even self-orthogonal codes.
Key wordsself-orthogonal codes spinor groups flat connections equivariant cohomology Morse theory
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