On the Dimension of the Hull
Nicolas Sendrier
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Source: Crossref
Published: May 1, 1997
DOI: 10.1137/s0895480195294027
Open original source ↗Source abstract
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.
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