On the dimension of the hull

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...

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Bibliographic Details
Published in:SIAM journal on discrete mathematics 1997-05, Vol.10 (2), p.282-293
Main Author: SENDRIER, N
Format: Article
Language:English
Subjects:
Algebra
Codes
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Linear codes
Mathematics
Number theory
Sciences and techniques of general use
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Summary: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.
ISSN:0895-4801
1095-7146
DOI:10.1137/S0895480195294027