Antichain Codes |
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Authors: | Gérard D Cohen Sylvia B Encheva Gilles Zémor |
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Institution: | (1) ENST, 46 rue Barrault, 75634 Paris Cedex 13, France;(2) Stord/Haugesund College, Skaareg. 103, 5500 Haugesund, Norway |
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Abstract: | We show that almost all codes satisfy an antichain condition. This states that the minimum length of a two dimensional subcode of a code C increases if the subcode is constrained to contain a minimum weight codeword. In particular, almost no code satisfies the chain condition. In passing, we study the typical behaviour of codes with respect to generalized distances and show that almost all lie on a generalized Varshamov-Gilbert bound. |
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Keywords: | multinomial code generalized distances chain condition wire-tap channel |
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