Abstract
Extended Golay codes possess certain two-level structures which are important for decoding the codes. However, these ideal structures are not limited to Golay codes. Here, the structures are generalised to other linear codes, among which are a binary (20, 9, 7) code, a binary (32, 16, 8) code, a binary (40, 20, 8) code and a ternary (18, 9, 6) code. Similar to the Golay codes, there are also efficient decoding algorithms for these codes, which are sufficiently simple to enable decoding the derived codes by hand calculations.
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