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The dimensions of codes

✍ Scribed by Ogul Arslan

Book ID
108167268
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
167 KB
Volume
116
Category
Article
ISSN
0097-3165

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We prove that the average dimension of the hull (intersection of the code and its dual code) of the cyclic codes of given length n over a g i v en nite eld F q is either zero or of the same order as n, and it is zero if and only if n is a divisor of an integer of the form q m + 1 , m > 0.