Privacy Amplification Theorem for Noisy Main Channel
ISC '01 Proceedings of the 4th International Conference on Information Security
The average dimension of the hull of cyclic codes
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
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The hull [Assmus, Jr. and Key, Discrete Math., 83 (1990), pp. 161--187], [Assmus, Jr. and Key, Designs and Their Codes, Cambridge University Press, 1992, p. 43] of a linear code is defined to be its intersection with its dual. We give here the number of distinct q-ary linear codes which have a hull of given dimension.We will prove that, asymptotically, the proportion of q-ary codes whose hull has dimension l is a positive constant that depends only on l and q and consequently that the average dimension of the hull is asymptotically a positive constant depending only on q.