We introduce exceptionally simple decoding algorithms for the two extended Golay codes. The algorithms are based on recent methods of Conway and Curtis of finding the unique blocks containing five points in either the (5,8,24) Steiner system or the (5,6,12) Steiner system. These decoding methods are simple enough to enable decoding extended Golay codes by hand. Both of the methods involve relations between the extended Golay codes and other self-dual codes. Proofs are given explaining these relationships and why the decoding methods work. The decoding algorithms are explained and illustrated with many examples. [3 , chap. 12] has facts about the Mathieu group and some details about decoding the Golay codes.
[1]
R. T. Curtis,et al.
A new combinatorial approach to M24
,
1976,
Mathematical Proceedings of the Cambridge Philosophical Society.
[2]
Daniel M. Gordon.
Minimal permutation sets for decoding the binary Golay codes
,
1982,
IEEE Trans. Inf. Theory.
[3]
Jacques Wolfmann.
A permutation decoding of the (24, 12, 8) Golay code
,
1983,
IEEE Trans. Inf. Theory.
[4]
Ian F. Blake,et al.
Decoding the binary Golay code with miracle octad generators (Corresp.)
,
1978,
IEEE Trans. Inf. Theory.
[5]
V. Pless.
On the uniqueness of the Golay codes
,
1968
.
[6]
Gustav Solomon,et al.
A Golay puzzle
,
1983,
IEEE Trans. Inf. Theory.