Abstract
The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructed by a projective method which is related to the structure. In this correspondence, the binary (4n, n+2k, ≥min(8, n, 2d)) linear codes are resulted from quaternary (n, k, d) linear block codes. Based on the structure, the efficient maximum likelihood decoding algorithms can be presented correspondingly for the derived codes.
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