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On the symmetry of good nonlinear codes

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1 Author(s)

It is shown that there are arbitrarily long "good" (in the sense of Gilbert) binary block codes that are preserved under very large permutation groups. This result contrasts sharply with the properties of linear codes: it is conjectured that long cyclic codes are bad, and known that long affine-invariant codes are bad.

Published in:

IEEE Transactions on Information Theory  (Volume:16 ,  Issue: 5 )