Polar-Code Construction of Golay Codes

This letter proposes a reinterpretation of the classical binary Golay codes as Polar codes with additional inner permutations and puncturing. This establishes a novel relationship between algebraic codes and codes based on Kronecker products, like polar codes. Naturally, this construction also allows for polar-code-type decoding of the Golay codes using successive cancellation list decoding. Using the Golay code as a driving example, we conjecture that other algebraic codes may be represented in a similar way.